title: Judaizers

text: The inclusion of Gentiles into early Christianity posed a problem for the Jewish identity of some of the early Christians: the new Gentile converts were not required to be circumcised nor to observe the Mosaic Law. Circumcision in particular was regarded as a token of the membership of the Abrahamic covenant, and the most traditionalist faction of Jewish Christians (i.e., converted Pharisees) insisted that Gentile converts had to be circumcised as well. Paul insisted that faith in Christ (see also Faith or Faithfulness) was sufficient for salvation, therefore the Mosaic Law wasn't binding for the Gentiles.


title: Judaizers

text: In the New Testament, the Judaizers were a group of Jewish Christians who insisted that their co-religionists should follow the Mosaic Law and that Gentile converts to Christianity must first be circumcised (i.e. become Jewish through the ritual of a proselyte). Although such repressive and legalistic requirements may have made Christianity a much less appealing religious choice for the vast majority of Gentiles, the evidence afforded in Paul's Epistle to the Galatians exhibits that, initially, a significant number of the Galatian Gentile converts appeared disposed to adopt these restrictions; indeed, Paul strenuously labors throughout the letter to dissuade them from doing so (cf. , , , ).


title: Judaizers

text: Paul was severely critical of the Judaizers within the Early Church and harshly reprimanded them for their doctrines and behavior. Paul saw the Judaizers as being both dangerous to the spread of the Gospel and propagators of grievous doctrinal errors. Many of his letters included in the New Testament (the Pauline epistles) contain considerable material disputing the view of this faction and condemning its practitioners. Paul publicly condemned Peter for his seemingly ambivalent reaction to the Judaizers, embracing them publicly in places where their preaching was popular while holding the private opinion that their doctrines were erroneous (cf. , , , , , , ).


title: Judaizers

text: That Gentile Christians should obey the Law of Moses was the assumption of some Jewish Christians in the Early Church, as represented by the group of Pharisees who had converted to Christianity in . Paul opposed this position, concluding that Gentiles did not need to obey to the entire Law of Moses in order to become Christians. The conflict between Paul and his Judaizing opponents over this issue came to a head with the Council of Jerusalem. According to the account given in Acts , it was determined by the Great Commission that Gentile converts to Christianity did not have to go through circumcision to be saved; but in addressing the second question as to whether or not they should obey the Torah, James the Just, brother of Jesus encouraged the Gentiles to "abstain from things sacrificed to idols, and from blood, and from things strangled, and from fornication" ().


title: Judaizers

text: Paul also addressed this question in his Epistle to the Galatians, in which he condemned as "false believers" those who insisted that circumcision had to be followed for justification:


title: Judaizers

text: Also Paul warned the early Galatian church that gentile Christians who submit to circumcision will be alienated from Christ: "Indeed I, Paul, say to you that if you become circumcised, Christ will profit you nothing. And I testify again to every man who becomes circumcised that he is a debtor to keep the whole law. You have become estranged from Christ, you who attempt to be justified by law; you have fallen from grace." ().


title: Judaizers

text: The "Catholic Encyclopedia" notes: "Paul, on the other hand, not only did not object to the observance of the Mosaic Law, as long as it did not interfere with the liberty of the Gentiles, but he conformed to its prescriptions when occasion required (). Thus he shortly after circumcised Timothy (), and he was in the very act of observing the Mosaic ritual when he was arrested at Jerusalem ( sqq.)."


title: Judaizers

text: Paul, who called himself "Apostle to the Gentiles", criticised the practice of circumcision, perhaps as an entrance into the New Covenant of Jesus. In the case of Timothy, whose mother was a Jewish Christian but whose father was a Greek, Paul personally circumcised him "because of the Jews" that were in town. Some believe that he appeared to praise its value in , yet later in Romans 2 we see his point. In he also disputes the value of circumcision. Paul made his case to the Christians at Rome that circumcision no longer meant the physical, but a spiritual practice. He also wrote: "Circumcision is nothing and uncircumcision is nothing. Keeping God's commands is what counts."


title: Judaizers

text: Later Paul more explicitly denounced the practice, rejecting and condemning those Judaizers who promoted circumcision to Gentile Christians. He accused them of turning from the Spirit to the flesh: "Are you so foolish, that, whereas you began in the Spirit, you would now be made perfect by the flesh?" Paul warned that the advocates of circumcision as a condition of salvation were "false brothers". He accused the advocates of circumcision of wanting to make a good showing in the flesh, and of glorying or boasting of the flesh. Paul instead stressed a message of salvation through faith in Christ opposed to the submission under the Mosaic Law that constituted a New Covenant with God, which essentially provides a justification for Gentiles from the harsh edicts of the Law, a New Covenant that didn't require circumcision (see also Justification by faith, Pauline passages supporting antinomianism, Abrogation of Old Covenant laws).


title: Judaizers

text: His attitude towards circumcision varies between his outright hostility to what he calls "mutilation" in to praise in . However, such apparent discrepancies have led to a degree of skepticism about the reliability of Acts. Baur, Schwanbeck, De Wette, Davidson, Mayerhoff, Schleiermacher, Bleek, Krenkel, and others have opposed the authenticity of the Acts; an objection is drawn from the discrepancy between and . Some believe that Paul wrote the entire Epistle to the Galatians attacking circumcision, saying in chapter five: "Behold, I Paul say unto you, if ye be circumcised, Christ shall profit you nothing."


title: Judaizers

text: The division between the Jews who followed the Mosaic Law and were circumcised and the Gentiles who were uncircumcised was highlighted in his Epistle to the Galatians:


title: Judaizers

text: "Judaizer" occurs once in Josephus' "Jewish War" 2.18.2, referring to the First Jewish–Roman War (66-73), written around the year 75:


title: Judaizers

text: It occurs once in the Apostolic Fathers collection, in Ignatius's letter to the Magnesians 10:3 written around the year 100:


title: Judaizers

text: Judaizing teachers are strongly condemned in the Epistle of Barnabas. (Although it did not become part of the Christian Biblical canon, it was widely circulated among Christians in the first two centuries and is part of the Apostolic Fathers.) Whereas Paul acknowledged that the Law of Moses and its observance were good when used correctly ("the law is good, if one uses it lawfully", ), the Epistle of Barnabas condemns most Jewish practices, claiming that Jews had grossly misunderstood and misapplied the Law of Moses.


title: Judaizers

text: Justin Martyr (about 140) distinguishes two kinds of Jewish Christians: those who observe the Law of Moses, but do not require its observance of others — with these he would hold communion – and those who believe the Mosaic law to be obligatory on all, whom he considers heretics ("Dialogue with Trypho" 47).


title: Judaizers

text: According to Eusebius' "History of the Church" 4.5.3-4: the first 15 Bishops of Jerusalem were "of the circumcision", although this in all likelihood is simply stating that they were Jewish Christians (as opposed to gentile Christians), and that they observed biblical circumcision and thus likely the rest of Torah as well.


title: Judaizers

text: The eight homilies "Adversus Judaeos" ("against the Jews") of John Chrysostom (347 – 407) deal with the relationship between Christians, Jews and Judaizers.


title: Judaizers

text: The influence of the Judaizers in the church diminished significantly after the destruction of Jerusalem, when the Jewish-Christian community at Jerusalem was dispersed by the Romans during the First Jewish–Roman War. The Romans also dispersed the Jewish leadership in Jerusalem in 135 during the Bar Kokhba Revolt. Traditionally it is believed the Jerusalem Christians waited out the Jewish–Roman wars in Pella in the Decapolis. These setbacks however didn't necessarily mean an end to Jewish Christianity, any more than Valerian's Massacre of 258, (when he killed all Christian bishops, presbyters, and deacons, including Pope Sixtus II and Antipope Novatian and Cyprian of Carthage), meant an end to Roman Christianity.


title: Judaizers

text: The Latin verb "iudaizare" is used once in the Vulgate where the Greek verb "ioudaizein" occurs at Galatians 2:14. Augustine in his "Commentary on Galatians", describes Paul's opposition in Galatia as those "qui gentes cogebant iudaizare" – "who thought to make the Gentiles live in accordance with Jewish customs."


title: Judaizers

text: Christian groups following Jewish practices never completely vanished, although they had been designated as heretical by the 5th century.


title: Judaizers

text: Skhariya or Zacharias the Jew from Caffa led a sect of Judaizers in Russia. In 1480 Grand Prince Ivan III of Moscow invited some of Zacharias's prominent adherents to visit Moscow. The Judaizers enjoyed the support of high-ranking officials, of statesmen, of merchants, of Yelena Stefanovna (wife of Ivan the Young, heir to the throne) and of Ivan's favorite deacon and diplomat Fyodor Kuritsyn. The latter even decided to establish his own club in the mid-1480s. However, in the end Ivan III renounced his ideas of secularization and allied with the Orthodox Christian clergy. The struggle against the adherents was led by hegumen Joseph Volotsky and his followers (иосифляне, iosiflyane or Josephinians) and by Archbishop Gennady of Novgorod. After uncovering adherents in Novgorod around 1487, Gennady wrote a series of letters to other churchmen over several years calling on them to convene "sobors" ("church councils") with the intention "not to debate them, but to burn them". Such councils took place in 1488, 1490, 1494 and 1504. The councils outlawed religious and non-religious books and initiated their burning, sentenced a number of people to death, sent adherents into exile, and excommunicated them. In 1491 Zacharias the Jew was executed in Novgorod by the order of Ivan III.


title: Judaizers

text: At various times since then, the Russian Orthodox Church has described several related Spiritual Christian groups as having a Judaizing character; the accuracy of this label – which was influenced by the early Christian polemics against Judaizers – has been disputed. The most famous of the Russian Empire's Judaizing sects were the Karaimites


title: Judaizers

text: or Karaimizing-Subbotniks like Alexander Zaïd (1886-1938) who successfully settled in the Holy Land from 1904.


title: Judaizers

text: The Epistle to the Galatians strongly influenced Martin Luther at the time of the Protestant Reformation because of its exposition of justification by grace. Nevertheless, various sects of Messianic Jews such as Jews for Jesus have managed to stake out territory for themselves in the Protestant camp.


title: Judaizers

text: This behavior was particularly persecuted from 1300 to 1800 during the Spanish and Portuguese Inquisitions, using as a basis the many references in the Pauline epistles regarding the "Law as a curse" and the futility of relying on the Law for attaining salvation, known as legalism. Thus, in spite of Paul's agreement at the Council of Jerusalem, gentile Christianity came to understand that any Torah Laws (with the exception of the Ten Commandments) were anathema, not only to gentile Christians but also to Christians of Jewish extraction. Under the Spanish Inquisition, the penalty to a converted Jew for "Judaizing" was usually death by burning.


title: Judaizers

text: The Spanish word "Judaizante" was applied both to Jewish "conversos" to Catholicism who practiced Judaism secretly and sometimes to Jews who had not converted, in Spain and the New World at the time of the Spanish Inquisition.


title: Judaizers

text: The term "Judaizers" was used by the Spanish Inquisition and the inquisitions established in Mexico City, Lima, and Cartagena de Indias for Conversos (also termed Marranos) accused of continuing to observe the Jewish religion, as Crypto-Jews. Entry of Portuguese New Christians into Spain and the Spanish realms occurred during the Union of Crowns of Spain and Portugal, 1580–1640, when both kingdoms and their overseas empires were held by the same monarch. The Bnei Anusim are modern day Hispanic Judaizers.


title: Judaizers

text: The Coptic, Ethiopian and Eritrean Orthodox Churches all continue to practice male circumcision. In Torah-submissive Christian groups which include the Ethiopian Orthodox church, dietary laws and Saturday Sabbath are observed as well.


title: Peter Snow

text: Peter John Snow (born 20 April 1938) is a British radio and television presenter and historian. Between 1969 and 2005, he was an analyst of general election results, first on ITV and later for the BBC. He presented "Newsnight" from its launch in 1980 until 1997. He has presented a number of documentaries, including some with his son, Dan Snow.


title: Peter Snow

text: Snow was born in Dublin, the son of John FitzGerald Snow and Margaret Mary Pringle. He is the grandson of First World War general Sir Thomas D'Oyly Snow; first cousin of Jon Snow, the presenter of "Channel 4 News" from 1989 to 2021; nephew of schoolmaster and bishop George D'Oyly Snow; and brother-in-law of historian-writer Margaret MacMillan. He is the father of fellow TV presenter Dan Snow.


title: Peter Snow

text: He spent part of his early childhood in Benghazi, Libya, where his father was stationed. His father became deputy Fortress commander at Gibraltar in 1956.


title: Peter Snow

text: Snow was educated at Wellington College, an independent school in the village of Crowthorne in Berkshire, and subsequently read Greats at Balliol College, Oxford, where he was taught by classicist and ancient historian Russell Meiggs and moral philosopher R. M. Hare. From 1956 to 1958 he did National Service as a junior officer in the Somerset Light Infantry, serving in Plymouth and Warminster.


title: Peter Snow

text: Snow was a foreign correspondent, Defence and Diplomatic Correspondent, and occasional newscaster for Britain's Independent Television News (ITN). He also appeared as an election analyst and co-presenter of ITN's General Election programmes throughout the late 1960s and 1970s. He joined the organisation in 1962. He gained a much higher profile after he was recruited in 1979 to be the main presenter of the new late evening BBC 2 in-depth news programme "Newsnight", which began almost a year later than planned, in January 1980. He left "Newsnight" in 1997 and presented "Tomorrow's World" (with Philippa Forrester) and the BBC Radio 4 quizzes "Masterteam" and "Brain of Britain", amongst other projects. At the Royal Television Society in 1998, Snow won the Judges' Award for services to broadcasting.


title: Peter Snow

text: Snow has been involved as an election analyst and co-presenter in the live General Election results programmes for many years, first at ITN for five General Elections (1966–1979) and later at the BBC for a further six (1983–2005). He presented in-depth statistical analyses of the election results at both ITN and the BBC, and at the BBC took over responsibility for this in 1983, following the death of Robert McKenzie, and became largely associated with McKenzie's BBC "Swingometer" when it was reinstated in 1992. In his presenting, he often made use of props and graphics. During the Falklands War in 1982 and the First Gulf War in early 1991, he used a sandpit to illustrate the progress of the combat. In 1994, he parodied his election role by providing analysis of the entries for the Eurovision Song Contest in the BBC's two contest preview shows ahead of the final in Dublin. His data analysis predicted that either France or the United Kingdom would win. They finished seventh and tenth respectively.


title: Peter Snow

text: Snow survived a plane crash at Port Blakely, Bainbridge Island, Washington on 1 October 1999 when the de Havilland Canada DHC-2 Beaver, registration number N9766Z, in which he was a passenger hit trees during a film project for the BBC.


title: Peter Snow

text: Along with his son, Dan, Snow presented 'Battleplan: El Alamein' for the BBC in October 2002 to celebrate the 60th anniversary of the allied defeat of Rommel's Afrika Korps. They then went on in 2004 to make the eight-part BBC series "Battlefield Britain", covering battles on British soil from Boudicca's struggle with the Romans to the Battle of Britain. They demonstrated the hardships that the much smaller soldiers must have faced (Peter is 6'5" and Dan is 6'6"). They reunited to host "20th Century Battlefields" for BBC 2 and the Military Channel in 2006. This covered battles all around the world from the Battle of Amiens in the First World War in 1918 to the Gulf War of 1990–1, and was presented in similar fashion to the first Battlefield Britain. Peter and Dan Snow authored BBC books with the same titles to coincide with the TV shows.


title: Peter Snow

text: Peter and Dan Snow also presented "Whose Britain is it anyway?", a survey of the ownership of Britain's countryside, in 2006, "What makes Britain rich?" in early 2007 and "What Britain earns" in 2008. Peter and Dan have also made two history series for BBC Radio Four on the Black Prince, on Wellington's Peninsular War, and the story of the Royal Flying Corps. He also presented "Random Edition" over a number of years, a Radio Four programme that examined in detail the stories in a newspaper chosen at random from one day in history.


title: Peter Snow

text: On 6 October 2005, the BBC announced that Snow would cease working on election broadcasts. Snow said "I shall be over 70 at the next general election and that, frankly, is a bit old to be dancing around in front of huge graphic displays." In July 2006, Snow presented "Pompeii Live" for Channel 5, a live outside broadcast telling the story of the Roman towns of Pompeii and Herculaneum. In January 2008, while presenting "What Britain Earns", a BBC programme about salaries in the UK alongside his son, Snow admitted to earning around £100,000 a year. In the summer of 2008, Peter presented a six part series for Channel 5, "Brits who Made the Modern World", a celebration of great twentieth century British engineers and inventors. In August 2008, Snow appeared in the reality TV talent show-themed television series, "Maestro" on BBC Two.


title: Peter Snow

text: In July 2009, to coincide with the 40th anniversary of the NASA moon landings, ITN produced five special 10-minute programmes for ITV titled "Mission to the Moon – News from 1969". Snow participated in these programmes, acting as a correspondent alongside former ITN colleague John Suchet, the presenter of the specials. Snow also presented a special on BBC Radio 4 focusing on "Britain's First Day of War in 1939". In June 2013, Snow presented "D-Day As it Happens" for Channel 4.


title: Peter Snow

text: In July 2016, Snow presented Trainspotting Live – a three part television series about trains and trainspotting on BBC Four.


title: Peter Snow

text: In June 2018 Peter presented a five-part series for Channel Four 'Great Train Restorations' which created a so-called Time Train from four refurbished railway carriages.


title: Peter Snow

text: In addition to presenting programmes, Snow has written a number of books besides the ones written with his son, Dan. In 1970, he wrote "Leila’s Hijack War" with a journalist colleague, David Phillips, telling the story of the international crisis that was caused by Palestinian guerrillas, including Leila Khaled, who hijacked three airliners and blew them up on a desert airstrip. In 1972, he wrote "Hussein", the Biography of King Hussein of Jordan. In 2010. Snow published "To War with Wellington", the story of the Iron Duke's campaigns from Portugal to Waterloo. In 2013, he published "When Britain burned the White House", the story of the 1814 British invasion of Washington.


title: Peter Snow

text: In 2015, he published "The Battle of Waterloo Experience" with his son Dan on the occasion of the bicentenary of the Battle of Waterloo in June 1815. In 2016, they went on to write "Treasures of British History, The Nation's History told through its 50 Most Important Documents".


title: Peter Snow

text: In 2017, Peter and his wife, Ann MacMillan of the Canadian Broadcasting Corporation (CBC), wrote "War Stories, Gripping Tales of Courage, Cunning and Compassion", which was published by John Murray.


title: Peter Snow

text: In 2020, Peter and Ann wrote "Treasures of World History, the Story of Civilisation in 50 documents" published by Welbeck.


title: Peter Snow

text: On the show "Horrible Histories", a regular sketch in the show, 'HHTV News' featuring Bob Hale, is a character whose personality is similar to that of Peter Snow. He is known for his catchphrases 'But not for long!' and 'Or so we thought!' and usually concludes with a summary but then starts talking more.


title: Peter Snow

text: Snow has been married twice, and has six children from three relationships. His eldest son, French citizen Matthieu, was born before his first marriage, although Snow was not aware of his existence until he was an adult. He married Alison Carter in 1964 and the couple had a son (Shane) and a daughter (Shuna). They divorced nine years later.


title: Peter Snow

text: In 1976 Snow married Ann MacMillan (of the Canadian Broadcasting Corporation since 1981), with whom he has a son, Dan (who is married to Lady Edwina Grosvenor, daughter of the 6th Duke of Westminster), and two daughters, Rebecca and Kate. His wife and sister-in-law are great-granddaughters of former British Prime Minister David Lloyd George.


title: Peter Snow

text: Snow was appointed Commander of the Order of the British Empire (CBE) in the 2006 New Year Honours for his services to Broadcasting. His hobbies include model railways, and he has an OO gauge layout installed in his loft. In August 2014, Snow was one of 200 public figures who were signatories to a letter to "The Guardian" expressing their hope that Scotland would vote to remain part of the United Kingdom in September's referendum on that issue.


title: Independent set (graph theory)

text: In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set formula_1 of vertices such that for every two vertices in formula_1, there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in formula_1. A set is independent if and only if it is a clique in the graph's complement. The size of an independent set is the number of vertices it contains. Independent sets have also been called "internally stable sets", of which "stable set" is a shortening.


title: Independent set (graph theory)

text: A maximal independent set is an independent set that is not a proper subset of any other independent set.


title: Independent set (graph theory)

text: A maximum independent set is an independent set of largest possible size for a given graph formula_4. This size is called the independence number of "formula_4" and is usually denoted by formula_6. The optimization problem of finding such a set is called the maximum independent set problem. It is a strongly NP-hard problem. As such, it is unlikely that there exists an efficient algorithm for finding a maximum independent set of a graph.


title: Independent set (graph theory)

text: Every maximum independent set also is maximal, but the converse implication does not necessarily hold.


title: Independent set (graph theory)

text: A set is independent if and only if it is a clique in the graph’s complement, so the two concepts are complementary. In fact, sufficiently large graphs with no large cliques have large independent sets, a theme that is explored in Ramsey theory.


title: Independent set (graph theory)

text: A set is independent if and only if its complement is a vertex cover. Therefore, the sum of the size of the largest independent set formula_6 and the size of a minimum vertex cover formula_8 is equal to the number of vertices in the graph.


title: Independent set (graph theory)

text: A vertex coloring of a graph formula_4 corresponds to a partition of its vertex set into independent subsets. Hence the minimal number of colors needed in a vertex coloring, the "chromatic number" formula_10, is at least the quotient of the number of vertices in formula_4 and the independent number formula_6.


title: Independent set (graph theory)

text: In a bipartite graph with no isolated vertices, the number of vertices in a maximum independent set equals the number of edges in a minimum edge covering; this is Kőnig's theorem.


title: Independent set (graph theory)

text: An independent set that is not a proper subset of another independent set is called "maximal". Such sets are dominating sets. Every graph contains at most 3 maximal independent sets, but many graphs have far fewer.


title: Independent set (graph theory)

text: The number of maximal independent sets in "n"-vertex cycle graphs is given by the Perrin numbers, and the number of maximal independent sets in "n"-vertex path graphs is given by the Padovan sequence. Therefore, both numbers are proportional to powers of 1.324718..., the plastic number.


title: Independent set (graph theory)

text: The first three of these problems are all important in practical applications; the independent set decision problem is not, but is necessary in order to apply the theory of NP-completeness to problems related to independent sets.


title: Independent set (graph theory)

text: The independent set problem and the clique problem are complementary: a clique in "G" is an independent set in the complement graph of "G" and vice versa. Therefore, many computational results may be applied equally well to either problem. For example, the results related to the clique problem have the following corollaries:


title: Independent set (graph theory)

text: Despite the close relationship between maximum cliques and maximum independent sets in arbitrary graphs, the independent set and clique problems may be very different when restricted to special classes of graphs. For instance, for sparse graphs (graphs in which the number of edges is at most a constant times the number of vertices in any subgraph), the maximum clique has bounded size and may be found exactly in linear time; however, for the same classes of graphs, or even for the more restricted class of bounded degree graphs, finding the maximum independent set is MAXSNP-complete, implying that, for some constant "c" (depending on the degree) it is NP-hard to find an approximate solution that comes within a factor of "c" of the optimum.


title: Independent set (graph theory)

text: The maximum independent set problem is NP-hard. However, it can be solved more efficiently than the O("n" 2) time that would be given by a naive brute force algorithm that examines every vertex subset and checks whether it is an independent set.


title: Independent set (graph theory)

text: As of 2017 it can be solved in time O(1.1996) using polynomial space. When restricted to graphs with maximum degree 3, it can be solved in time O(1.0836).


title: Independent set (graph theory)

text: Modular decomposition is a good tool for solving the maximum weight independent set problem; the linear time algorithm on cographs is the basic example for that. Another important tool are clique separators as described by Tarjan.


title: Independent set (graph theory)

text: Kőnig's theorem implies that in a bipartite graph the maximum independent set can be found in polynomial time using a bipartite matching algorithm.


title: Independent set (graph theory)

text: In general, the maximum independent set problem cannot be approximated to a constant factor in polynomial time (unless P = NP). In fact, Max Independent Set in general is Poly-APX-complete, meaning it is as hard as any problem that can be approximated to a polynomial factor. However, there are efficient approximation algorithms for restricted classes of graphs.


title: Independent set (graph theory)

text: In planar graphs, the maximum independent set may be approximated to within any approximation ratio "c" < 1 in polynomial time; similar polynomial-time approximation schemes exist in any family of graphs closed under taking minors.


title: Independent set (graph theory)

text: In bounded degree graphs, effective approximation algorithms are known with approximation ratios that are constant for a fixed value of the maximum degree; for instance, a greedy algorithm that forms a maximal independent set by, at each step, choosing the minimum degree vertex in the graph and removing its neighbors, achieves an approximation ratio of (Δ+2)/3 on graphs with maximum degree Δ. Approximation hardness bounds for such instances were proven in . Indeed, even Max Independent Set on 3-regular 3-edge-colorable graphs is APX-complete.


title: Independent set (graph theory)

text: An interval graph is a graph in which the nodes are 1-dimensional intervals (e.g. time intervals) and there is an edge between two intervals if and only if they intersect. An independent set in an interval graph is just a set of non-overlapping intervals. The problem of finding maximum independent sets in interval graphs has been studied, for example, in the context of job scheduling: given a set of jobs that has to be executed on a computer, find a maximum set of jobs that can be executed without interfering with each other. This problem can be solved exactly in polynomial time using earliest deadline first scheduling.


title: Independent set (graph theory)

text: A geometric intersection graph is a graph in which the nodes are geometric shapes and there is an edge between two shapes if and only if they intersect. An independent set in a geometric intersection graph is just a set of disjoint (non-overlapping) shapes. The problem of finding maximum independent sets in geometric intersection graphs has been studied, for example, in the context of Automatic label placement: given a set of locations in a map, find a maximum set of disjoint rectangular labels near these locations.


title: Independent set (graph theory)

text: Finding a maximum independent set in intersection graphs is still NP-complete, but it is easier to approximate than the general maximum independent set problem. A recent survey can be found in the introduction of .


title: Independent set (graph theory)

text: The problem of finding a maximal independent set can be solved in polynomial time by a trivial greedy algorithm. All maximal independent sets can be found in time O(3) = O(1.4423).


title: Independent set (graph theory)

text: The maximum independent set and its complement, the minimum vertex cover problem, is involved in proving the computational complexity of many theoretical problems. They also serve as useful models for real world optimization problems, for example maximum independent set is a useful model for discovering stable genetic components for designing engineered genetic systems.


title: Book of Joel

text: The Book of Joel is collected as one of the twelve minor prophets of the Nevi'im ("Prophets") in the Hebrew Bible, and as a book in its own right in the Christian Old Testament.


title: Book of Joel

text: After a superscription ascribing the prophecy to Joel (son of Pethuel), the book may be broken down into the following sections:


title: Book of Joel

text: The Book of Joel's division into chapters and verses differs widely between editions of the Bible; some editions have three chapters, others four. Translations with four chapters include: the Jewish Publication Society's version of the Hebrew Bible (1917), Jerusalem Bible (1966), New American Bible (Revised Edition, 1970), Complete Jewish Bible (1998), Tree of Life Version (2015)


title: Book of Joel

text: In the 1611 King James Bible, the Book of Joel is formed by three chapters: the second one has 32 verses, and it is equivalent to the union of the chapter 2 (with 26 verses) and chapter 3 (with 5 verses) of other editions of the Bible.


title: Book of Joel

text: As there are no explicit references in the book to datable persons or events, scholars have assigned a wide range of dates to the book. The main positions are:


title: Book of Joel

text: Evidence produced for these positions includes allusions in the book to the wider world, similarities with other prophets, and linguistic details. Some commentators, such as John Calvin, attach no great importance to the precise dating.


title: Book of Joel

text: Joel 1 and 2 are preserved in the Dead Sea Scrolls, in fragmentary manuscripts 4Q78, 4Q82, and the Scroll Wadi Muraba’at.


title: Book of Joel

text: The Masoretic text places Joel between Hosea and Amos (the order inherited by the Tanakh and Old Testament), while the Septuagint order is Hosea–Amos–Micah–Joel–Obadiah–Jonah. The Hebrew text of Joel seems to have suffered little from scribal transmission, but is at a few points supplemented by the Septuagint, Syriac, and Vulgate versions, or by conjectural emendation. While the book purports to describe a plague of locusts, some ancient Jewish opinion saw the locusts as allegorical interpretations of Israel's enemies. This allegorical interpretation was applied to the church by many church fathers. Calvin took a literal interpretation of chapter 1, but allegorical view of chapter 2, a position echoed by some modern interpreters. Most modern interpreters, however, see Joel speaking of a literal locust plague given a prophetic/ apocalyptic interpretation.


title: Book of Joel

text: The traditional ascription of the whole book to the prophet Joel was challenged in the late nineteenth and early twentieth centuries by a theory of a three-stage process of composition: 1:1–2:27 were from the hand of Joel, and dealt with a contemporary issue; 2:28–3:21/3:1–4:21 were ascribed to a continuator with an apocalyptic outlook. Mentions in the first half of the book to the day of the Lord were also ascribed to this continuator. 3:4–8/4:4–8 could be seen as even later. Details of exact ascriptions differed between scholars.


title: Book of Joel

text: This splitting of the book's composition began to be challenged in the mid-twentieth century, with scholars defending the unity of the book, the plausibility of the prophet combining a contemporary and apocalyptic outlook, and later additions by the prophet. The authenticity of 3:4–8 has presented more challenges, although a number of scholars still defend it.


title: Book of Joel

text: There are many parallels of language between Joel and other Old Testament prophets. They may represent Joel's literary use of other prophets, or vice versa.


title: Book of Joel

text: In the New Testament, his prophecy of the outpouring of God's Holy Spirit upon all people was notably quoted by Saint Peter in his Pentecost sermon.


title: Book of Joel

text: Joel 3:10 / 4:10 is a variation of Isaiah 2:4 and Micah 4:3's prophecy, "They will beat their swords into plowshares and their spears into pruning hooks.", instead commanding, "Beat your plowshares into swords and your pruning hooks into spears."


title: Book of Joel

text: The table below represents some of the more explicit quotes and allusions between specific passages in Joel and passages from the Old and New Testaments.


title: Book of Joel

text: Plange quasi virgo ("Lament like a virgin"), the third responsory for Holy Saturday, is loosely based on verses from the Book of Joel: the title comes from Joel 1:8.


title: Saratoga, California

text: Saratoga is a city in Santa Clara County, California. Located in Silicon Valley, in the southern Bay Area, its population was 31,051 at the 2020 census. Saratoga is an affluent residential community, known for its wineries, restaurants, and attractions like Villa Montalvo, Mountain Winery, and Hakone Gardens.


title: Saratoga, California

text: The area comprising Saratoga was earlier inhabited by the Ohlone Native Americans. In 1847, European settlers created a settlement at what is now Saratoga when William Campbell (father of Benjamin Campbell, the founder of nearby Campbell, California), constructed a sawmill about southeast of the present downtown area. An early map noted the area as Campbell's Gap.


title: Saratoga, California

text: In 1851, Martin McCarthy, who had leased the mill, built a toll road down to the Santa Clara Valley, and founded what is now Saratoga as "McCarthysville". The toll gate was located at the present-day intersection of Big Basin Way and 3rd St., giving the town its first widely used name: "Toll Gate". In 1867 the town received a post office under the name of "McCarthysville".


title: Saratoga, California

text: Early residents, who moved to Saratoga in 1881, were Mary Brown (1816–1884), widow of John Brown the abolitionist, her daughters Sarah and Ellen, and the husband of the latter, James Fablinger. All are buried in Madronia Cemetery.


title: Saratoga, California

text: Industry soon sprang up and at its pinnacle, the town had a furniture factory, grist mill, tannery, and a paper factory. To commemorate this newfound productivity, the town was renamed again in 1863 as "Bank Mills". In the 1850s, Jud Caldwell discovered springs which were called "Pacific Congress Springs" because the water had a mineral content similar to "Congress Springs" in Saratoga Springs, New York. In 1865 the town received its final name, "Saratoga", after the city in New York. At the same time a resort hotel called "Congress Hall" was constructed at the springs, named after the famous resort "Congress Hall" at Saratoga Springs, New York. California's "Congress Hall" attracted tourists to the area until it burned down in 1903. These events would eventually lead to Saratoga being listed as a California Historical Landmark in 1950.


title: Saratoga, California

text: Saratoga became agricultural, as did much of the rest of the valley; a few vineyards and orchards from this period remain today. After World War II the town quickly became urbanized, and it incorporated in 1956 mostly to avoid being annexed by San Jose. A slogan during the campaign to incorporate the city of Saratoga was "Keep it rural," according to historian Willys I. Peck. Today the city serves as a bedroom community for upper-middle class and upper class Silicon Valley tech workers and executives.


title: Saratoga, California

text: Saratoga drew notoriety for the suicide of Audrie Pott, a 15-year-old Saratoga High School student, September 2012. The three teenagers charged with sexually assaulting Pott pleaded guilty and served time in juvenile hall for the sexual assault.


title: Saratoga, California

text: Saratoga is bordered by Cupertino and San Jose to the north, a small portion of Campbell and Los Gatos to the east, and Monte Sereno to the southeast. Saratoga is located at . According to the United States Census Bureau, the city has a total area of , all of it land. Within its borders, Saratoga includes lush redwood forests, foothills suitable for wine grapes and sunny valley floor once covered with prune and apricot orchards, now with suburban homes, schools and churches.


title: Saratoga, California

text: Neighborhoods in Saratoga include Brookview and Pride's Crossing in the north part of the city, Blue Hills and Greenbrier in the northwest area, and Congress Springs in the southwestern corner of Saratoga. The Golden Triangle, a name invented by real estate agents, is an area bounded by Saratoga Avenue, Saratoga-Sunnyvale Road and Cox Avenue. The Golden Triangle consists mostly of four-bedroom ranch homes (with values ranging from between $1 to $3 million) on quarter acre lots that are gradually being replaced by Mediterranean custom designs. Northeast of the Golden Triangle is a neighborhood known as Saratoga Woods, a small community located behind Prospect High School north of Cox. Bellgrove Circle is a popular neighborhood located next to highway 85. The land of Bellgrove Circle, once used as a vineyard, was previously owned by Paul Masson Winery and is east of Saratoga Avenue and north of Rt 85. Kentfield is south of Rt 85 and also east of Saratoga Avenue. Parker Ranch is a very affluent neighborhood with minimum lots, west of Saratoga-Sunnyvale Road and up into the hills. The downtown area along Big Basin Way is known as the Village.


title: Saratoga, California

text: The 2010 United States Census reported that Saratoga had a population of 29,926. The population density was . The racial makeup of Saratoga was 16,125 (53.9%) White, 94 (0.3%) African American, 41 (0.1%) Native American, 12,376 (41.4%) Asian, 23 (0.1%) Pacific Islander, 202 (0.7%) from other races, and 1,065 (3.6%) from two or more races. There were 1,034 Hispanic or Latino residents of any race (3.5%).


title: Saratoga, California

text: The Census reported that 29,727 people (99.3% of the population) lived in households, 34 (0.1%) lived in non-institutionalized group quarters, and 165 (0.6%) were institutionalized.


title: Saratoga, California

text: There were 10,734 households, out of which 4,024 (37.5%) had children under the age of 18 living in them, 7,893 (73.5%) were opposite-sex married couples living together, 608 (5.7%) had a female householder with no husband present, 213 (2.0%) had a male householder with no wife present. There were 159 (1.5%) unmarried opposite-sex partnerships, and 44 (0.4%) same-sex married couples or partnerships. 1,740 households (16.2%) were made up of individuals, and 1,115 (10.4%) had someone living alone who was 65 years of age or older. The average household size was 2.77. There were 8,714 families (81.2% of all households); the average family size was 3.11.


title: Saratoga, California

text: In Saratoga, 7,173 people (24.0%) were under the age of 18, 1,390 people (4.6%) were aged 18 to 24, 4,678 people (15.6%) were aged 25 to 44, 10,598 people (35.4%) aged 45 to 64, and 6,087 people (20.3%) who were 65 years of age or older. The median age was 47.8 years. For every 100 females, there were 95.7 males. For every 100 females age 18 and over, there were 92.6 males.


title: Saratoga, California

text: There were 11,123 housing units at an average density of , of which 9,258 (86.2%) were owner-occupied, and 1,476 (13.8%) were occupied by renters. The homeowner vacancy rate was 0.7%; the rental vacancy rate was 4.3%. 26,201 people (87.6% of the population) lived in owner-occupied housing units and 3,526 people (11.8%) lived in rental housing units.


title: Saratoga, California

text: In 2011, "Bloomberg Businessweek" reported that the average household income was $237,804 with an average household net worth of $1,516,018.


title: Saratoga, California

text: As of the census of 2000, there were 29,843 people, 10,450 households, and 8,600 families residing in the city. The population density was 951.5/km (2,465.3/mi). There were 10,649 housing units at an average density of 339.5/km (879.7/mi). The racial makeup of the city was 67.39% White, 0.39% African American, 0.15% Native American, 29.08% Asian, 0.08% Pacific Islander, 0.57% from other races, and 2.33% from two or more races. 3.14% of the population were Hispanic or Latino of any race.


title: Saratoga, California

text: There were 10,450 households, out of which 38.7% had children under the age of 18 living with them, 75.0% were married couples living together, 4.9% had a female householder with no husband present, and 17.7% were non-families. 14.3% of all households were made up of individuals, and 7.6% had someone living alone who was 65 years of age or older. The average household size was 2.83 and the average family size was 3.13. The population-age distribution was as follows: 26.0% under the age of 18, 4.0% from 18 to 24, 23.8% from 25 to 44, 29.9% from 45 to 64, and 16.3% who were 65 years of age or older. The median age was 43 years. For every 100 females, there were 96.5 males. For every 100 females age 18 and over, there were 92.6 males.


title: Saratoga, California

text: According to a 2007 estimate the median income for a household in the city was $137,270, and the median income for a family was $159,765. Males had a median income of $75,000 versus $66,240 for females. The per capita income for the city was $65,400. About 1.8% of families and 2.8% of the population were below the poverty line, including 3.2% of those under age 18 and 2.6% over 64.


title: Saratoga, California

text: The 2016 Coldwell Banker Home Listing Report listed Saratoga as the most expensive housing market in the United States. In 2010, Bloomberg Businessweek named Saratoga the most expensive suburb in California. According to CNN Money, 70.42% of Saratoga households have an income greater than $100,000.


title: Saratoga, California

text: Saratoga was ranked by "Forbes" in 2009 as one of America's top 20 most-educated small towns. "Bloomberg Businessweek" named Saratoga's zip code 95070 the 18th richest zip code in America in 2011. In 2018, data from the American Community Survey revealed that Saratoga was the 8th wealthiest city in the United States.


title: Saratoga, California

text: Saratoga is a general law city under California law, meaning that the organization and powers of the city are established by state law. It has a council–manager form of government. The current mayor is Yan Zhao. Vice Mayor is Tina Walia. Other current council members are Mary-Lynne Bernald, Kookie Fitzsimmons, and Rishi Kumar.


title: Saratoga, California

text: The Saratoga City Council has had to make many controversial decisions in a community with residents known to be protectionist of their existing exclusivity. The council was a leader in dealing with the unfunded pension crisis in California.


title: Saratoga, California

text: In the California State Legislature, Saratoga is in , and in . In the United States House of Representatives, Saratoga is in .


title: Saratoga, California

text: Various public school districts serve Saratoga. At elementary level (grades K to 8) these include Saratoga Union School District, Campbell Union School District, Cupertino Union School District and Moreland School District. High school districts that serve Saratoga include the Los Gatos-Saratoga Joint Union High School District, Fremont Union High School District and Campbell Union High School District. These districts provide a number of high schools including


title: Saratoga, California

text: Saratoga High School, Monta Vista High School (located in Cupertino but servicing a portion of Saratoga), Lynbrook High School (located in San Jose but servicing a portion of Saratoga as well), Prospect High School and Westmont High School (located in Campbell but servicing a portion of Saratoga).


title: Saratoga, California

text: Private schools in the area include Challenger School, Saint Andrew's School, and Sacred Heart School.


title: Saratoga, California

text: West Valley Community College provides college-level education in the district whilst the Santa Clara County Library District operates the Saratoga Library.


title: Saratoga, California

text: The original alignment of Highway 85 along Saratoga-Sunnyvale Road was deleted in 1994 when the West Valley Freeway was completed, and it passes through northeast Saratoga. Highway 85 has one onramp/offramp within the city, at Saratoga Avenue; while the original plans for the freeway also included exits at Quito Road and Prospect Avenue, objections by residents kept those interchanges from being constructed. Street signs are brown in color.


title: Saratoga, California

text: The Union Pacific Railroad operates freight through the town, servicing the nearby Permanente Quarry. The rail line travels parallel to Route 85. Passenger trains, including the Peninsular Railway, operated starting in 1908, delivering commuters to San Francisco in 90 minutes. Saratoga currently has no passenger train service; it has minimal bus service.


title: Saratoga, California

text: Saratoga also has a zoning code aimed at preserving a semi-rural appearance. Saratoga emphasizes its semi-rural appearance by foregoing street lights and sidewalks on most residential streets. This contributes to Saratoga's high housing costs.


title: Saratoga, California

text: The Blue Hills neighborhood of Saratoga has many hiking trails for use by residents that are owned by the City of Saratoga.


title: Trade route

text: A trade route is a logistical network identified as a series of pathways and stoppages used for the commercial transport of cargo. The term can also be used to refer to trade over bodies of water. Allowing goods to reach distant markets, a single trade route contains long-distance arteries, which may further be connected to smaller networks of commercial and noncommercial transportation routes. Among notable trade routes was the Amber Road, which served as a dependable network for long-distance trade. Maritime trade along the Spice Route became prominent during the Middle Ages, when nations resorted to military means for control of this influential route. During the Middle Ages, organizations such as the Hanseatic League, aimed at protecting interests of the merchants and trade became increasingly prominent.


title: Trade route

text: In modern times, commercial activity shifted from the major trade routes of the Old World to newer routes between modern nation-states. This activity was sometimes carried out without traditional protection of trade and under international free-trade agreements, which allowed commercial goods to cross borders with relaxed restrictions. Innovative transportation of modern times includes pipeline transport and the relatively well-known trade involving rail routes, automobiles, and cargo airlines.


title: Trade route

text: Long-distance trade routes were developed in the Chalcolithic Period. The period from the middle of the 2nd millennium BCE to the beginning of the Common Era saw societies in Southeast Asia, Western Asia, the Mediterranean, China, and the Indian subcontinent develop major transportation networks for trade.


title: Trade route

text: One of the vital instruments which facilitated long-distance trade was portage and the domestication of beasts of burden. Organized caravans, visible by the 2nd millennium BCE, could carry goods across a large distance as fodder was mostly available along the way. The domestication of camels allowed Arabian nomads to control the long-distance trade in spices and silk from the Far East to the Arabian Peninsula. Caravans were useful in long-distance trade largely for carrying luxury goods, the transportation of cheaper goods across large distances was not profitable for caravan operators. With productive developments in iron and bronze technologies, newer trade routes – dispensing innovations of civilizations – began to rise.


title: Trade route

text: Navigation was known in Sumer between the 4th and the 3rd millennium BCE. The Egyptians had trade routes through the Red Sea, importing spices from the "Land of Punt" (East Africa) and from Arabia.


title: Trade route

text: In Asia, the earliest evidence of maritime trade was the Neolithic trade networks of the Austronesian peoples among which is the "lingling-o" jade industry of the Philippines, Taiwan, southern Vietnam, and peninsular Thailand. It also included the long-distance routes of Austronesian traders from Indonesia and Malaysia connecting China with South Asia and the Middle East since approximately 500 BCE. It facilitated the spread of Southeast Asian spices and Chinese goods to the west, as well as the spread of Hinduism and Buddhism to the east. This route would later become known as the Maritime Silk Road, although that is a misnomer, since spices, rather than silk, were traded along this route. Many Austronesian technologies like the outrigger and catamaran, as well as Austronesian ship terminologies, still persist in many of the coastal cultures in the Indian Ocean.


title: Trade route

text: Maritime trade began with safer coastal trade and evolved with the manipulation of the monsoon winds, soon resulting in trade crossing boundaries such as the Arabian Sea and the Bay of Bengal. South Asia had multiple maritime trade routes which connected it to Southeast Asia, thereby making the control of one route resulting in maritime monopoly difficult. Indian connections to various Southeast Asian states buffered it from blockages on other routes. By making use of the maritime trade routes, bulk commodity trade became possible for the Romans in the 2nd century BCE. A Roman trading vessel could span the Mediterranean in a month at one-sixtieth the cost of over-land routes.


title: Trade route

text: The peninsula of Anatolia lay on the commercial land routes to Europe from Asia as well as the sea route from the Mediterranean to the Black Sea. Records from the 19th century BCE attest to the existence of an Assyrian merchant colony at Kanesh in Cappadocia (now in modern Turkey). Trading networks of the Old World included the Grand Trunk Road of India and the Incense Road of Arabia. A transportation network consisting of hard-surfaced highways, using concrete made from volcanic ash and lime, was built by the Romans as early as 312 BCE, during the times of the Censor Appius Claudius Caecus. Parts of the Mediterranean world, Roman Britain, Tigris-Euphrates river system and North Africa fell under the reach of this network at some point of their history.


title: Trade route

text: "The spread of urban trading networks, and their extension along the Persian Gulf and eastern Mediterranean, created a complex molecular structure of regional foci so that as well as the zonation of core and periphery (originally created around Mesopotamia) there was a series of interacting civilizations: Mesopotamia, Egypt, the Indus Valley; then also Syria, central Anatolia (Hittites) and the Aegean (Minoans and Mycenaeans). Beyond this was a margin which included not only temperate areas such as Europe, but the dry steppe corridor of central Asia. This was truly a world system, even though it occupied only a restricted portion of the western Old World. Whilst each civilization emphasized its ideological autonomy, all were identifiably part of a common world of interacting components."


title: Trade route

text: These routes – spreading religion, trade and technology – have historically been vital to the growth of urban civilization. The extent of development of cities, and the level of their integration into a larger world system, has often been attributed to their position in various active transport networks.


title: Trade route

text: The Incense Route served as a channel for trading of Indian, Arabian and East Asian goods. The incense trade flourished from South Arabia to the Mediterranean between roughly the 3rd century BCE to the 2nd century CE. This trade was crucial to the economy of Yemen and the frankincense and myrrh trees were seen as a source of wealth by its rulers.


title: Trade route

text: Ptolemy II Philadelphus, emperor of Ptolemaic Egypt, may have forged an alliance with the Lihyanites in order to secure the incense route at Dedan, thereby rerouting the incense trade from Dedan to the coast along the Red Sea to Egypt. I. E. S. Edwards connects the Syro-Ephraimite War to the desire of the Israelites and the Aramaeans to control the northern end of the Incense route, which ran up from Southern Arabia and could be tapped by commanding Transjordan.


title: Trade route

text: Gerrha – inhabited by Chaldean exiles from Babylon – controlled the Incense trade routes across Arabia to the Mediterranean and exercised control over the trading of aromatics to Babylon in the 1st century BCE. The Nabateans exercised control over the routes along the Incense Route, and their hold was challenged – without success – by Antigonus Cyclops, emperor of Syria. The Nabatean control over trade further increased and spread in many directions.


title: Trade route

text: The replacement of Greece by the Roman empire as the administrator of the Mediterranean basin led to the resumption of direct trade with the East and the elimination of the taxes extracted previously by the middlemen of the south. According to Milo Kearney (2003) "The South Arabs in protest took to pirate attacks over the Roman ships in the Gulf of Aden. In response, the Romans destroyed Aden and favored the Western Abyssinian coast of the Red Sea." Indian ships sailed to Egypt as the maritime routes of Southern Asia were not under the control of a single power.


title: Trade route

text: Some similarities between the Mesoamerican and the Andean cultures suggest that the two regions became a part of a wider world system, as a result of trade, by the 1st millennium BCE. The current academic view is that the flow of goods across the Andean slopes was controlled by institutions distributing locations to local groups, who were then free to access them for trading. This trade across the Andean slopes – described sometimes as "vertical trade" – may have overshadowed the long-distance trade between the people of the Andes and the neighboring forests. The Callawaya herbalists traded in tropical plants between 6th and the 10th centuries, while copper was dealt by specialized merchants in the Peruvian valley of Chincha. Long-distance trade may have seen local elites resorting to struggle in order for manipulation and control.


title: Trade route

text: Prior to the Inca dominance, specialized long-distance merchants provided the highlanders with goods such as gold nuggets, copper hatchets, cocoa, salt etc. for redistribution among the locals, and were key players in the politics of the region. Hatchet shaped copper currency was produced by the Peruvian people, in order to obtain valuables from pre Columbian Ecuador. A maritime exchange system stretched from the west coast of Mexico to southernmost Peru, trading mostly in Spondylus, which represented rain and fertility and was considered the principal food of the gods by the people of the Inca empire. Spondylus was used in elite rituals, and the effective redistribution of it had political effect in the Andes during the pre-Hispanic times.


title: Trade route

text: The Silk Road was one of the first trade routes to join the Eastern and the Western worlds. According to Vadime Elisseeff (2000):


title: Trade route

text: "Along the Silk Roads, technology traveled, ideas were exchanged, and friendship and understanding between East and West were experienced for the first time on a large scale. Easterners were exposed to Western ideas and life-styles, and Westerners, too, learned about Eastern culture and its spirituality-oriented cosmology. Buddhism as an Eastern religion received international attention through the Silk Roads."


title: Trade route

text: Cultural interactions patronized often by powerful emperors, such as Kanishka, led to development of art due to introduction of a rich variety of influences. Buddhist missions thrived along the Silk Roads, partly due to the conducive intermixing of trade and cultural values, which created a series of safe stoppages for both the pilgrims and the traders. Among the frequented routes of the Silk Route was the Burmese route extending from Bhamo, which served as a path for Marco Polo's visit to Yunnan and Indian Buddhist missions to Canton in order to establish Buddhist monasteries. This route – often under the presence of hostile tribes – also finds mention in the works of Rashid-al-Din Hamadani.


title: Trade route

text: The Grand Trunk Road – connecting Chittagong in Bangladesh to Peshawar in Pakistan – has existed for over two and a half millennia. One of the important trade routes of the world, this road has been a strategic artery with fortresses, halting posts, wells, post offices, milestones and other facilities. Part of this road through Pakistan also coincided with the Silk Road.


title: Trade route

text: This highway has been associated with emperors Chandragupta Maurya and Sher Shah Suri, the latter became synonymous with this route due to his role in ensuring the safety of the travelers and the upkeep of the road. Emperor Sher Shah widened and realigned the road to other routes, and provided approximately 1700 roadside inns through his empire. These inns provided free food and lodgings to the travelers regardless of their status.


title: Trade route

text: The British occupation of this road was of special significance for the British Raj in India. Bridges, pathways and newer inns were constructed by the British for the first thirty-seven years of their reign since the occupation of Punjab in 1849. The British followed roughly the same alignment as the old routes, and at some places the newer routes ran parallel to the older routes.


title: Trade route

text: "Along this road marched not only the mighty armies of conquerors, but also the caravans of traders, scholars, artists, and common folk. Together with people, moved ideas, languages, customs, and cultures, not just in one, but in both directions. At different meeting places – permanent as well as temporary – people of different origins and from different cultural backgrounds, professing different faiths and creeds, eating different foods, wearing different clothes, and speaking different languages and dialects would meet one another peacefully. They would understand one another's food, dress, manner, and etiquette, and even borrow words, phrases, idioms and, at times, whole languages from others."


title: Trade route

text: The Amber Road was a European trade route associated with the trade and transport of amber. Amber satisfied the criteria for long-distance trade as it was light in weight and was in high demand for ornamental purposes around the Mediterranean. Before the establishment of Roman control over areas such as Pannonia, the Amber Road was virtually the only route available for long-distance trade.


title: Trade route

text: Towns along the Amber Road began to rise steadily during the 1st century CE, despite the troop movements under Titus Flavius Vespasianus and his son Titus Flavius Domitianus.


title: Trade route

text: Under the reign of Tiberius Caesar Augustus, the Amber Road was straightened and paved according to the prevailing urban standards. Roman towns began to appear along the road, initially founded near the site of Celtic "oppida".


title: Trade route

text: The 3rd century saw the Danube river become the principal artery of trade, eclipsing the Amber Road and other commercial routes. The redirection of investment to the Danubian forts saw the towns along the Amber Road growing slowly, though yet retaining their prosperity. The prolonged struggle between the Romans and the barbarians further left its mark on the towns along the Amber Road.


title: Trade route

text: Via Maris, literally Latin for "the way of the sea", was an ancient highway used by the Romans and the Crusaders. The states controlling the Via Maris were in a position to grant access for trade to their own citizens and collect tolls from the outsiders to maintain the trade route. The name "Via Maris" is a Latin translation of a Hebrew phrase related to Isaiah. Due to the biblical significance of this ancient route, many attempts to find its present-day location have been made by Christian pilgrims. 13th-century traveler and pilgrim Burchard of Mount Zion refers to the Via Maris route as a way leading along the shore of the Sea of Galilee.


title: Trade route

text: Early Muslim writings confirm that the people of West Africa operated a sophisticated network of trade, usually under the authority of a monarch who levied taxes and provided bureaucratic and military support to his kingdom. Sophisticated mechanisms for the economic and political development of the involved African areas were in place before Islam further strengthened trade, towns and government in western Africa. The capital, court and trade of the region find mention in the works of scholar Abū 'Ubayd 'Abd Allāh al-Bakrī; the mainstay of the trans Saharan trade was gold and salt.


title: Trade route

text: The powerful Saharan tribes, Berber in origin and later adapting to Muslim and Arab cultures, controlled the channels to western Africa by making efficient use of horse-drawn vehicles and pack animals. The Songhai engaged in a struggle against the Sa'di dynasty of Morocco over the control of the trans Saharan trade, resulting in damage on both sides and a weak Moroccan victory, further strengthening the uninvolved Saharan tribes. Struggles and disturbances continued till the 14th century, by which the Mandé merchants were trading with the Hausa, between Lake Chad and the Niger. Newer trade routes developed following extension of trade.


title: Trade route

text: The first true maritime trade network in the Indian Ocean was by the Austronesian peoples of Island Southeast Asia. They established trade routes with Southern India and Sri Lanka as early as 500 BCE, ushering an exchange of material culture (like catamarans, outrigger boats, sewn-plank boats, and paan) and cultigens (like coconuts, sandalwood, bananas, and sugarcane); as well as connecting the material cultures of India and China. They constituted the majority of the Indian Ocean component of the spice trade network. Indonesians, in particular were trading in spices (mainly cinnamon and cassia) with East Africa using catamaran and outrigger boats and sailing with the help of the Westerlies in the Indian Ocean. This trade network expanded to reach as far as Africa and the Arabian Peninsula, resulting in the Austronesian colonization of Madagascar by the first half of the first millennium AD. It continued up to historic times, later becoming the Maritime Silk Road. This trade network also included smaller trade routes within Island Southeast Asia, including the lingling-o jade network, and the trepanging network.


title: Trade route

text: In eastern Austronesia, various traditional maritime trade networks also existed. Among them was the ancient Lapita trade network of Island Melanesia; the Hiri trade cycle, Sepik Coast exchange, and the Kula ring of Papua New Guinea; the ancient trading voyages in Micronesia between the Mariana Islands and the Caroline Islands (and possibly also New Guinea and the Philippines); and the vast inter-island trade networks of Polynesia.


title: Trade route

text: The Ptolemaic dynasty (305 to 30 BC) had initiated Greco-Roman maritime trade contact with India using the Red Sea ports. The Roman historian Strabo mentions a vast increase in trade following the Roman annexation of Egypt, indicating that monsoon was known and manipulated for trade in his time. By the time of Augustus up to 120 ships were setting sail every year from Myos Hormos to India, trading in a diverse variety of goods. Arsinoe, Berenice Troglodytica and Myos Hormos were the principal Roman ports involved in this maritime trading network, while the Indian ports included Barbaricum, Barygaza, Muziris and Arikamedu.


title: Trade route

text: The Indians were present in Alexandria and the Christian and Jewish settlers from Rome continued to live in India long after the fall of the Roman empire, which resulted in Rome's loss of the Red Sea ports, previously used to secure trade with India by the Greco-Roman world since the time of the Ptolemaic dynasty.


title: Trade route

text: Shortly before the 12th century the Germans played a relatively modest role in the north European trade. However, this was to change with the development of Hanseatic trade, as a result of which German traders became prominent in the Baltic and the North Sea regions. Following the death of Eric VI of Denmark, German forces attacked and sacked Denmark, bringing with them artisans and merchants under the new administration which controlled the Hansa regions. During the third quarter of the 14th century the Hanseatic trade faced two major difficulties: economic conflict with the Flanders and hostilities with Denmark. These events led to the formation of an organized association of Hanseatic towns, which replaced the earlier union of German merchants. This new Hansa of the towns, aimed at protecting interests of the merchants and trade, was prominent for the next hundred and fifty years.


title: Trade route

text: Philippe Dollinger associates the downfall of the Hansa to a new alliance between Lübeck, Hamburg and Bremen, which outshadowed the older institution. He further sets the date of dissolution of the Hansa at 1630 and concludes that the Hansa was almost entirely forgotten by the end of the 18th century. Scholar Georg Friedrich Sartorius published the first monograph regarding the community in the early years of the 19th century.


title: Trade route

text: The trade route from the Varangians to the Greeks (, "Put' iz varyag v greki", , , "Emporikḗ Odós Varángōn-Ellḗnōn") was a trade route that connected Scandinavia, Kievan Rus' and the Byzantine Empire. The route allowed traders along the route to establish a direct prosperous trade with Byzantium, and prompted some of them to settle in the territories of present-day Belarus, Russia and Ukraine.


title: Trade route

text: The route began in Scandinavian trading centres such as Birka, Hedeby, and Gotland, crossed the Baltic Sea entered the Gulf of Finland, followed the Neva River into the Lake Ladoga. Then it followed the Volkhov River, upstream past the towns of Staraya Ladoga and Velikiy Novgorod, crossed Lake Ilmen, and up the Lovat River. From there, ships had to be portaged to the Dnieper River near Gnezdovo. A second route from the Baltic to the Dnieper was along the Western Dvina (Daugava) between the Lovat and the Dnieper in the Smolensk region, and along the Kasplya River to Gnezdovo. Along the Dnieper, the route crossed several major rapids and passed through Kiev, and after entering the Black Sea followed its west coast to Constantinople.


title: Trade route

text: The economic growth of Europe around the year 1000, together with the lack of safety on the mainland trading routes, eased the development of major commercial routes along the coast of the Mediterranean. The growing independence of some coastal cities gave them a leading role in this commerce: Maritime Republics, Italian ""Repubbliche Marinare"" (Venice, Genoa, Amalfi, Pisa, Gaeta, Ancona and Ragusa), developed their own "empires" in the Mediterranean shores.


title: Trade route

text: From the 8th until the 15th century, they held the monopoly of European trade with the Middle East. The silk and spice trade, involving spices, incense, herbs, drugs and opium, made these Mediterranean city-states phenomenally rich. Spices were among the most expensive and demanded products of the Middle Ages. They were all imported from Asia and Africa. Muslim traders – mainly descendants of Arab sailors from Yemen and Oman – dominated maritime routes throughout the Indian Ocean, tapping source regions in the Far East and shipping for trading emporiums in India, westward to Ormus in Persian Gulf and Jeddah in the Red Sea. From there, overland routes led to the Mediterranean coasts. Venetian merchants distributed then the goods through Europe until the rise of the Ottoman Empire, that eventually led to the fall of Constantinople in 1453, barring Europeans from important combined-land-sea routes.


title: Trade route

text: As trade between India and the Greco-Roman world increased spices became the main import from India to the Western world, bypassing silk and other commodities. The Indian commercial connection with South East Asia proved vital to the merchants of Arabia and Persia during the 7th and 8th centuries.


title: Trade route

text: The Abbasids used Alexandria, Damietta, Aden and Siraf as entry ports to India and China. Merchants arriving from India in the port city of Aden paid tribute in form of musk, camphor, ambergris and sandalwood to Ibn Ziyad, the sultan of Yemen. Moluccan products shipped across the ports of Arabia to the Near East passed through the ports of India and Sri Lanka. Indian exports of spices find mention in the works of Ibn Khurdadhbeh (850 CE), al-Ghafiqi (1150), Ishak bin Imaran (907) and Al Kalkashandi (14th century). After reaching either the Indian or the Sri Lankan ports, spices were sometimes shipped to East Africa, where they were used for many purposes, including burial rites.


title: Trade route

text: On the orders of Manuel I of Portugal, four vessels under the command of navigator Vasco da Gama rounded the Cape of Good Hope, continuing to the eastern coast of Africa to Malindi to sail across the Indian Ocean to Calicut. The wealth of the Indies was now open for the Europeans to explore; the Portuguese Empire was one of the early European empires to grow from spice trade.


title: Trade route

text: The Maritime Jade Road was an extensive trading network connecting multiple areas in Southeast and East Asia. Its primary products were made of jade mined from Taiwan by animist Taiwanese indigenous peoples and processed mostly in the Philippines by animist indigenous Filipinos, especially in Batanes, Luzon, and Palawan. Some were also processed in Vietnam, while the peoples of Malaysia, Brunei, Singapore, Thailand, Indonesia, and Cambodia also participated in the massive animist-led trading network. Participants in the network at the time had a majority animist population. The maritime road is one of the most extensive sea-based trade networks of a single geological material in the prehistoric world. It was in existence for at least 3,000 years, where its peak production was from 2000 BCE to 500 CE, older than the Silk Road in mainland Eurasia or the later Maritime Silk Road. A notable artifact that the trading network made, the Lingling-o artifacts, were made by artisans around 500 BCE. The network began to wane during its final centuries from 500 CE until 1000 CE. The entire period of the network was a golden age for the diverse animist societies of the region.


title: Trade route

text: The Maritime Silk Road refers to the maritime section of historic Silk Road that connects China, Southeast Asia, the Indian subcontinent, Arabian peninsula, Somalia and all the way to Egypt and finally Europe. It flourished between 2nd-century BCE and 15th-century CE. Despite its association with China in recent centuries, the Maritime Silk Road was primarily established and operated by Austronesian sailors in Southeast Asia, and by Persian and Arab traders in the Arabian Sea.


title: Trade route

text: The Maritime Silk Road developed from the earlier Austronesian spice trade networks of Islander Southeast Asians with Sri Lanka and Southern India (established 1000 to 600 BCE), as well as the earlier Maritime Jade Road, known for "lingling-o" artifacts, in Southeast Asia, based in Taiwan and the Philippines. For most of its history, Austronesian thalassocracies controlled the flow of the Maritime Silk Road, especially the polities around the straits of Malacca and Bangka, the Malay Peninsula, and the Mekong Delta; although Chinese records misidentified these kingdoms as being "Indian" due to the Indianization of these regions. Prior to the 10th century, the route was primarily used by Southeast Asian traders, although Tamil and Persian traders also sailed them. The route was influential in the early spread of Hinduism and Buddhism to the east.


title: Trade route

text: China later built its own fleets starting from the Song dynasty in the 10th century, participating directly in the trade route up until the end of the Colonial Era and the collapse of the Qing dynasty.


title: Trade route

text: The modern times saw development of newer means of transport and often controversial free trade agreements, which altered the political and logistical approach prevalent during the Middle Ages. Newer means of transport led to the establishment of new routes, and countries opened up borders to allow trade in mutually agreed goods as per the prevailing free trade agreement. Some old trading route were reopened during the modern times, although in different political and logistical scenarios. The entry of harmful foreign pollutants by the way of trade routes has been a cause of alarm during the modern times. A conservative estimate stresses that future damages from harmful animal and plant diseases may be as high as 134 billion US dollars in the absence of effective measures to prevent the introduction of unwanted pests through various trade routes.


title: Trade route

text: Networks, like the Santa Fe Trail and the Oregon Trail, became prominent in the United States with wagon trains gaining popularity as a mode of long-distance overland transportation for both people and goods. The Oregon–California routes were highly organized with planned rendezvous locations and essential supplies. The settlers in the United States used these wagon trains – sometimes made up of 100 of more Conestoga wagons – for westward emigration during the 18th and the 19th centuries. Among the challenges faced by the wagon route operators were crossing rivers, mountains and hostile Native Americans. Preparations were also made according to the weather and protection of trade and travelers was ensured by a few guards on horseback.


title: Trade route

text: Wagon freighting was also essential to American growth until it was replaced by the railroad and the truck.


title: Trade route

text: The 1844 Railway act of England compelled at least one train to a station every day with the third class fares priced at a penny a mile. Trade benefited as the workers and the lower classes had the ability to travel to other towns frequently. Suburban communities began to develop and towns began to spread outwards. The British constructed a vast railway network in India, but it was considered to serve a strategic purpose in addition to the commercial purpose. The efficient use of rail routes helped in the unification of the United States of America, and the first transcontinental railroad was completed in 1869.


title: Trade route

text: The modern times saw nations struggle for the control of rail routes: The Trans-Siberian Railway was intended to be used by the Russian government for control of Manchuria and later China; the German forces wanted to establish Berlin-Baghdad Railway in order to influence the Near East; and the Austrian government planned a route from Vienna to Salonika for control of the Balkans.


title: Trade route

text: Railroads reached their maturity in the early 20th century, as trains carried the bulk of land freight and passenger traffic in the industrialized countries of the world. By the mid-20th century, however, they had lost their preeminent position. The private automobile had replaced the railroad for short passenger trips, while the airplane had usurped it for long-distance travel, especially in the United States. Railroads remained effective, however, for transporting people in high-volume situations, such as commuting between the centres of large cities and their suburbs, and medium-distance travel of less than about 300 miles between urban centres.


title: Trade route

text: Although railroads have lost much of the general-freight-carrying business to semi-trailer trucks, they remain the best means of transporting large volumes of such bulk commodities as coal, grain, chemicals, and ore over long distances. The development of containerization has made the railroads more effective in handling finished merchandise at relatively high speeds. In addition, the introduction of piggyback flatcars, in which truck trailers are transported long distances on specially-designed cars, has allowed railroads to regain some of the business lost to trucking.


title: Trade route

text: The advent motor vehicles created a demand for better use of highways. Roads evolved into two way roads, expressways, freeways and tollways during the modern times. Existing roads were developed and highways were designed according to intended use.


title: Trade route

text: Trucks came into widespread use in the Western World during World War I, and quickly gained reputation as a means of long-distance transportation of goods. Modern highways, such as the Trans-Canada Highway, Highway 1 (Australia) and Pan-American Highway allowed transport of goods and services across great distances. Automobiles continue to play a crucial role in the economies of the Industrialized countries, resulting in rise of businesses such as motor freight operation and truck transportation.


title: Trade route

text: The emission rate for cars using highways has been on a decline between 1975 and 1995 due to regulations and the introduction of unleaded petrol. This trend is especially notable since there has been a growth in vehicles and vehicle miles traveled by automobiles using these highways.


title: Trade route

text: A consistent shift from land based trade to sea-based trade has been recorded since the last three millennia. The strategic advantages of port cities as trading centers are many: they are both less dependent on vital connections and less vulnerable to blockages. Oceanic ports can help forge trading relationships with other parts of the world easily.


title: Trade route

text: Modern maritime trade routes – sometimes in the form of artificial canals like the Suez Canal – had visible impact on the economic and political standing of nations. The opening of the Suez Canal altered British interactions with the colonies of the British Empire as the dynamics of transportation, trade and communication had now changed drastically. Other waterways, like the Panama Canal played an important role in the histories of many nations. Inland water transportation remained significantly important even as the advent of railroads and automobiles resulted in a steady decline of canals. Inland water transport is still used for the transportation of bulk commodities e.g. grains, coal, and ore.


title: Trade route

text: Waterway commerce was historically important to Europe, particularly to Russia. According to the "Encyclopædia Britannica" (2002): "Russia has been a significant beneficiary. Not only have inland waterways opened vast areas of its interior to development, but Moscow – linked to the White, Baltic, Black, Caspian, and Azov seas by canals and rivers – has become a major inland port."


title: Trade route

text: Oil spills are recorded both in case of maritime routes and pipeline routes to the main refineries. Oil spills, amounting to as much as 7.56 billion liters of oil entering the oceans every year, occur due to damaged equipment or human error.


title: Trade route

text: The 21st Century Maritime Silk Road is a current project of the Chinese government to expand and intensify trade on the maritime Silk Road. This is leading to major investments in ports, traffic routes and other infrastructure in Europe and Africa as well. The maritime silk road essentially runs from the Chinese coast to Singapore and Kuala Lumpur, via the Sri Lankan Colombo towards the southern tip of India, to the East African Mombasa, from there to Djibouti, then via the Suez Canal to the Mediterranean, there via Haifa, Istanbul and Athens to the Upper Adriatic region to the northern Italian hub of Trieste with its international free port and its rail connections to Central and Eastern Europe and the North Sea.


title: Trade route

text: Historically, many governments followed a policy of protection of trade. International free trade became visible in 1860 with the Anglo-French commercial treaty, and the trend gained further momentum during the period after World War II.


title: Trade route

text: "After World War II, strong sentiment developed throughout the world against protection and high tariffs and in favor of freer trade. The results were new organizations and agreements on international trade such as the General Agreement on Tariffs and Trade (1948), the Benelux Economic Union (1948), the European Economic Community (Common Market, 1957), the European Free Trade Association (1959), Mercosur (the Southern Cone Common Market, 1991), and the World Trade Organization (1995). In 1993, the North American Free Trade Agreement (NAFTA) was approved by the governments of Canada, Mexico, and the United States. In the early 1990s, the nations of the European Union (the successor organization to the Common Market) undertook to remove all barriers to the free movement of trade and employment across their mutual borders."


title: Trade route

text: In May 2004 the United States of America signed the American Free trade Agreement with five Central American nations.


title: Trade route

text: Air transport has become an indispensable part of modern society. People have come to use air transport both for long and middle distances, with the average route length of long distances being 720 kilometers in Europe and 1220 kilometers in the US. This industry annually carries 1.6 billion passengers worldwide, covers a 15 million kilometer network, and has an annual turnover of 260 billion dollars.


title: Trade route

text: This mode of transportation links national, international and global economies, making it vital to many other industries. Newer trends of liberalization of trade have fostered routes among nations bound by agreements. One such example, the American Open Skies policy, led to greater openness in many international markets, but some international restrictions have survived even during the present times.


title: Trade route

text: Express delivery through international cargo airlines touched US$20 billion in 1998 and, according to the World Trade Organization, is expected to triple in 2015. In 1998, 50 pure cargo-service companies operated internationally.


title: Trade route

text: Air transport particularly favors light, expensive and small products: electronic media rather than books, for example, and refined drugs rather than bulk food.


title: Trade route

text: The economic importance of pipeline transport – responsible for a high percentage of oil and natural gas transportation – is often unrecognized by the general public due to the lack of visibility of this mode. Generally held to be safer and more economical and reliable than the other modes of transport, this mode has many advantages over rival modes, such as trucks and railways. Examples of modern pipeline transport include Alashankou-Dushanzi Crude Oil Pipeline and Iran-Armenia Natural Gas Pipeline. International pipeline transport projects, like the Baku-Tbilisi-Ceyhan pipeline, presently connect modern nation states – in this case, Azerbaijan, Georgia and Turkey – through pipeline networks.


title: Trade route

text: In some select cases, pipelines can even transport solids, such as coal and other minerals, over long distances; short-distance transportation of goods such as grain, cement, concrete, solid wastes, pulp etc. is also feasible.


title: Cross-platform play

text: In video games with online gaming functionality, also called cross-compatible play, cross-platform play, crossplay, or cross-play describes the ability of players using different video game hardware to play with each other simultaneously. It is commonly applied to the ability for players using a game on a specific video game console to play alongside a player on a different hardware platform such as another console or a computer. A related concept is cross-save, where the player's progress in a game is stored in separate servers, and can be continued in the game but on a different hardware platform.


title: Cross-platform play

text: Cross-play is related to but distinct from the notion of cross-platform development, which uses software languages and tools to enable deployment of software on multiple platforms. Cross-platform play is also a distinct concept from the ability to allow a player to play a game on different hardware platforms, often only having to purchase the title for one single system to have access to it on other systems, and retaining their progress in the game through the use of cloud storage or similar techniques.


title: Cross-platform play

text: Cross-platform play, while technically feasible with today's computer hardware, generally is impeded by two factors. One factor is the difference in control schemes between personal computers and consoles, with the keyboard-and-mouse controls typically giving computer players an advantage that cannot be easily remedied. The second factor relates to the closed online services used on consoles that are designed to provide a safe and consistent environment for its players that require the businesses' cooperation to open up for cross-platform play. Up through September 2018, Sony Interactive Entertainment had restricted PlayStation 4 cross-platform play with other consoles, creating a rift between players of popular games like "Rocket League" and "Fortnite Battle Royale". In September 2018, Sony changed their stance, and had opened up beta-testing for "Fortnite" cross-platform play. Sony officially stated it will allow any developers to support cross-platform play in October 2019.


title: Cross-platform play

text: Prior to the seventh generation of video game consoles, video games were typically developed for a single console with only a few games receiving cross-platform releases across multiple consoles. This was due to the unique processing architecture of each console, making development for each a closed ecosystem and requiring additional effort to port to other systems. With the seventh generation of consoles, which saw console systems use similar processor hardware as personal computers, cross-platform development for both consoles and personal computers became much easier to achieve using standard software libraries, game engines, and scripting languages that isolate platform-specific details from the specific elements for the game itself. Such tools enabled games to be released simultaneously for multiple platforms.


title: Cross-platform play

text: With the availability of the Internet, games have included online multiplayer components, allowing two or more users to play simultaneously on different computer systems. Games released for a platform may be able to take advantage of platform-specific networking libraries to accomplish this, such as the Winsock layer for Microsoft Windows. These games would not be able to be played cross-platform with other versions released on other systems. Instead, most games with online components and developed for multiple platforms generally use standard TCP/IP-type functions for communication between players' clients, or between a client and a game server, nullifying the intrinsic differences between hardware platforms.


title: Cross-platform play

text: There are some practical limitations for cross-platform play. In games where the player's computer or console acts as the server, the hardware capabilities may place limits on the number of players that that server can host, and thus preventing cross-platform play. Hardware also plays an issue in considering how much the player can customize the game on a computer to run at a high framerate, while console versions are fixed to run at the optimal experience on the set hardware configuration.


title: Cross-platform play

text: The most common limitation for supporting cross-platform play from a developer's stance is the difference in control schemes between consoles and computers. Computers with keyboard and mouse controls on personal computers are generally considered to have a significant advantage in games that require aiming, such as first-person shooters, over analog controllers for consoles. Console games are then subsequently developed with features such as aim assist to make up for the lack of precision controls. In 2010, Rahul Sood, the president of Voodoo PC, stated that Microsoft had terminated cross-platform play between Xbox 360 and computer players for an upcoming game claiming that even skilled console players "got destroyed every time" in matches against computer players of mediocre skill due to the difference between controller and keyboard-and-mouse controls, and thus would be seen as an embarrassment to the Xbox 360. Microsoft's Senior Director of Computer and Mobile Gaming Kevin Unangst countered this point, stating that Microsoft's internal testing found that much of the issues related to control scheme difference can be mitigated through a game's design and balance. Blizzard Entertainment implemented cross-platform play in its game "Overwatch" for all supported consoles and on personal computers, but due to the advantage keyboard-mouse players have over controllers, which greatly affects performance in the fast-paced game, they kept the game's competitive play mode segregated into console and computer player pools. Cliff Bleszinski believed that cross-platform play for his game "LawBreakers" was a "pipe dream", as he anticipated that by placing tools such as aim assist to help console players match computer players, computer players would be upset at the handicap this introduced, and the player base would react negatively towards this. Following wider adoption of cross-platform play in many mainstream titles starting around 2020, the issues of balancing the game with the use of aim assist in first-person shooters, where the game automatically locks onto targets for those using controllers, became of concern as a game with aggressive aim assist could lead to poor balance between cross-platform players.


title: Cross-platform play

text: Providing cross-platform play is seen as a means to keep a game's player base large even several months out after a game's release.


title: Cross-platform play

text: Generally, cross-platform play between personal computers of different operating systems is readily enabled using standard communication protocols, and only requires the game to be appropriately ported to these other systems; the computer platform is considered to be very open due to this. Though digital online services that operate on the computer have become popular since around 2010, these systems typically remain open, providing the developer with tools to take advantage of cross-platform play. For example, Valve's online game service, Steam was initially built for Windows computers, but in 2010 expanded to OS X systems, and in 2013 to Linux (including Valve's customized SteamOS). The Steamworks API offered to developers through the service enables cross-platform play to uses on these different operating systems while taking advantage of the friends, communication, and matchmaking features offered by Steam. With the introduction of the Epic Games Store, Epic Games released its own set of backend tools to support networking for games released on the store. Though initially games on both the Epic Games and Steam were not compatible, Epic developed and released a free API for supporting cross-platform play for games released on both storefronts in June 2022, with plans to expand this for mobile and console games.


title: Cross-platform play

text: Prior to 2006, hardware consoles typically lacked built-in Internet connections, often requiring special hardware to be able to connect to the Internet. This enabled some games to be deployed as cross-platform titles. Early attempts at cross-platform play include the 1998 Sega Dreamcast which included a built-in modem; Microsoft worked with Sega to provide a version of Windows CE to developers to make cross-platform games between Dreamcast and Windows players for games such as "4x4 Evo", "Maximum Pool", "Quake 3 Arena" and "Phantasy Star Online". Sony would launch the PlayStation 2 in 2000, which feature support for online play via an external modem. On September 13, 2001, "Capcom vs. SNK 2" was released for the Dreamcast and PlayStation 2 in Japan. The Japanese versions of the game allow players from both platforms to compete against each other online via KDDI's Multi-Matching service, making it the first game title to allow cross-play between game consoles from competing manufacturers. Square Enix would introduce online play between PlayStation 2 and Windows users for "Final Fantasy XI" in 2002.


title: Cross-platform play

text: The introduction of Internet-ready game consoles, such as Sony's PlayStation 3 and Microsoft's Xbox, brought online services that aid in securely managing the player's credentials, digital store purchases, friend lists, messaging and other social features, and online matchmaking for multiplayer games. Though providing benefits to the player, these online services also aid the managing company to maintain a consistent and attractive experience for its users, assuring games, updates, and other content meet both desirable quality and content restrictions as to draw new players to these consoles. Historically, cross-platform play with consoles has been very limited as a result of these services, and the ability to have console games with cross-platform play is considered to be a "holy grail" within the video game sector.


title: Cross-platform play

text: One technical challenge that faces console-based cross-platform play is the network communication between platforms, managing the different protocols used by each service. However, the technical limitations can be overcome, with at least three developers stating they could enable cross-platform play within a day once they were allowed to do so. A "configuration issue" briefly allowed computer, PlayStation 4, and Xbox One players to play alongside each other in the online cooperative game "Fortnite" in mid-September 2017. This had not been an expected feature of the game, as cited by the game's current specifications. While Epic Games corrected the configuration and stated this was a mistake, the brief situations demonstrated that technical barriers to cross-platform play can be met. Later in March 2018, Epic announced plans to take the spinoff title, "Fortnite Battle Royale" Windows, PlayStation 4, Xbox One, and mobile devices, with cross-platform play enabled between computer, PlayStation 4 and mobile, and computer, Xbox One, Nintendo Switch, and mobile.