We study an important practical aspect of the route planning problem in real-world road networks -- maneuvers. Informally, maneuvers represent various irregularities of the road network graph such as turn-prohibitions, traffic light delays, round-abouts, forbidden passages and so on. We propose a generalized model which can handle arbitrarily complex (and even negative) maneuvers, and outline how to enhance Dijkstra's algorithm in order to solve route planning queries in this model without prior adjustments of the underlying road network graph.
The first, and seemingly the simplest, solution is commonly used as it makes a road network graph maneuver-free and so there is no need to adjust the queries in any way. Unfortunately, it can significantly increase the size of the graph @cite_12 ; for instance, replacing a single turn-prohibition can add up to eight new vertices in place of one original @cite_9 . A solution like this one thus conflicts with the aforementioned (graph-size) objectives. Another approach @cite_10 uses so-called dual graph representation instead of the original one, where allowed turns are modeled by dual edges.
@cite_9 @cite_10 @cite_12
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We study approaches for the exact solution of the NP-hard minimum spanning tree problem under conflict constraints. Given a graph (G(V,E) ) and a set (C E E ) of conflicting edge pairs, the problem consists of finding a conflict-free minimum spanning tree, i.e. feasible solutions are allowed to include at most one of the edges from each pair in (C ). The problem was introduced recently in the literature, with several results on its complexity and approximability. Some formulations and both exact and heuristic algorithms were also discussed, but computational results indicate considerably large duality gaps and a lack of optimality certificates for benchmark instances. In this paper, we build on the representation of conflict constraints using an auxiliary conflict graph ( G (E,C) ), where stable sets correspond to conflict-free subsets of (E ). We introduce a general preprocessing method and a branch and cut algorithm using an IP formulation with exponentially sized classes of valid inequalities for both the spanning tree and the stable set polytopes. Encouraging computational results indicate that the dual bounds of our approach are significantly stronger than those previously available, already in the initial LP relaxation, and we are able to provide new feasibility and optimality certificates. In real road networks, the presence of no-left, no-right or no U-turn signs, restricts the movement of vehicles at intersections. These turn prohibitions must be considered when calculating the shortest path between a starting and an ending point in a road network. We propose an extension of Dijkstra’s algorithm to solve the shortest path problem with turn prohibitions. The method uses arc labeling and a network structure with low memory requirements. We compare the proposed method with the dual graph approach in a set of randomly generated networks and Bogota’s large-scale road network. Our computational experiments show that the performance of the proposed method is better than that of the dual graph approach, both in terms of computing time and memory requirements. We co-developed a Web-based decision support system for computing shortest paths with turn prohibitions that uses the proposed method as the core engine. The purpose of this paper is to describe the dual graph technique developed by the authors to represent transport networks. The method is intended to simplify the coding of complex transport networks to a considerable degree, particularly when there are turning restrictions, or when multiple transfers between modes or transit lines must be taken into account. A first section presents the traditional form in which transport networks are analytically represented, and describes the main problems that are confronted. In particular, the difficulty to represent prohibited turns is shown to be a major problem; when such a restriction is introduced, the representation of the network becomes increasingly complex and intractable, requiring a large number of fictitious links and nodes. A second section describes the dual graph technique in general terms, and shows how the network code remains simple, even if prohibited turns are introduced, completely avoiding fictitious links and the possibility of errors. A third section describes the way in which dual networks are constructed in formal terms. It is shown that the process of constructing the dual graph can be automated easily, becoming completely transparent to the model user. In a fourth section the method is extended to represent transit routes or, in general, multiple operators and modes. This is achieved by introducing further dimension to the dual network (multidimensional networks); the dual of very complex transit networks can also be automated, avoiding the need for fictitious nodes and links to represent transfer points. A final section draws the main conclusions and points out that dual graphs can be very useful for detailed traffic models. Brief references are made to other known methods to represent turn restrictions. In this paper a model that handles costs of turns in route planning is defined, investigated and discussed. Costs are traditionally attached to edges in a graph. For some important route planning problems other costs can be identified, namely costs that appear when leaving one edge and entering the next. Examples are turn restrictions, the turning angle, or the simple necessity to turn. Such costs cannot be stored as attributes of nodes or edges in the graph, and they cannot be handled correctly by shortest path algorithms without modifications. Turn costs can be represented by a pseudo-dual graph in a way that shortest path algorithms run without modifications. Although the idea is not new, it has not found much interest in the literature. The pseudo-dual graph is defined here in a new way, it is systematically investigated, and some practical applications are shown. Concentrating strictly on topology, it turns out that the pseudo-dual graph is conceptually cleaner and more efficient in route planning than alternative, currently used ways to deal with turn costs. The discussed applications are from the field of pedestrian navigation, which gave rise to this research. In the first part of this survey, we consider planar graphs that can be represented by a dissections of a rectangle into rectangles. In rectangular drawings, the corners of the rectangles represent the vertices. The graph obtained by taking the rectangles as vertices and contacts as edges is the rectangular dual. In visibility graphs and segment contact graphs, the vertices correspond to horizontal or to horizontal and vertical segments of the dissection. Special orientations of graphs turn out to be helpful when dealing with characterization and representation questions. Therefore, we look at orientations with prescribed degrees, bipolar orientations, separating decompositions, and transversal structures. How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an n-vertex graph, the names of the vertices (i.e., integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n vertices are just @math bit place holders to allow data on the edges to encode the structure of the graph. In this scenario, there is no such waste. By assigning @math bit labels to the vertices, the structure of the graph is completely encoded, so that, given the labels of two vertices, one can test if they are adjacent in time linear in the size of the labels. Furthermore, given an arbitrary original labeling of the vertices, structure coding labels are found (as above) that are no more than a small constant factor larger than the original labels. These notions are intimately related to vertex-induced universal graphs of polynomial size. For example, planar graphs can be labeled with structure coding labels of size @math , which i... Patent prior art search is a type of search in the patent domain where documents are searched for that describe the work previously carried out related to a patent application. The goal of this search is to check whether the idea in the patent application is novel. Vocabulary mismatch is one of the main problems of patent retrieval which results in low retrievability of similar documents for a given patent application. In this paper we show how the term distribution of the cited documents in an initially retrieved ranked list can be used to address the vocabulary mismatch. We propose a method for query modeling estimation which utilizes the citation links in a pseudo relevance feedback set. We first build a topic dependent citation graph, starting from the initially retrieved set of feedback documents and utilizing citation links of feedback documents to expand the set. We identify the important documents in the topic dependent citation graph using a citation analysis measure. We then use the term distribution of the documents in the citation graph to estimate a query model by identifying the distinguishing terms and their respective weights. We then use these terms to expand our original query. We use CLEF-IP 2011 collection to evaluate the effectiveness of our query modeling approach for prior art search. We also study the influence of different parameters on the performance of the proposed method. The experimental results demonstrate that the proposed approach significantly improves the recall over a state-of-the-art baseline which uses the link-based structure of the citation graph but not the term distribution of the cited documents. We study the problem of graph summarization. Given a large graph we aim at producing a concise lossy representation (a summary) that can be stored in main memory and used to approximately answer queries about the original graph much faster than by using the exact representation. In this work we study a very natural type of summary: the original set of vertices is partitioned into a small number of supernodes connected by superedges to form a complete weighted graph. The superedge weights are the edge densities between vertices in the corresponding supernodes. To quantify the dissimilarity between the original graph and a summary, we adopt the reconstruction error and the cut-norm error. By exposing a connection between graph summarization and geometric clustering problems (i.e., k-means and k-median), we develop the first polynomial-time approximation algorithms to compute the best possible summary of a certain size under both measures. We discuss how to use our summaries to store a (lossy or lossless) compressed graph representation and to approximately answer a large class of queries about the original graph, including adjacency, degree, eigenvector centrality, and triangle and subgraph counting. Using the summary to answer queries is very efficient as the running time to compute the answer depends on the number of supernodes in the summary, rather than the number of nodes in the original graph. In a constrained shortest path (CSP) query, each edge in the road network is associated with both a length and a cost. Given an origin s, a destination t, and a cost constraint θ, the goal is to find the shortest path from s to t whose total cost does not exceed θ. Because exact CSP is NP-hard, previous work mostly focuses on approximate solutions. Even so, existing methods are still prohibitively expensive for large road networks. Two main reasons are (i) that they fail to utilize the special properties of road networks and (ii) that most of them process queries without indices; the few existing indices consume large amounts of memory and yet have limited effectiveness in reducing query costs. Motivated by this, we propose COLA, the first practical solution for approximate CSP processing on large road networks. COLA exploits the facts that a road network can be effectively partitioned, and that there exists a relatively small set of landmark vertices that commonly appear in CSP results. Accordingly, COLA indexes the vertices lying on partition boundaries, and applies an on-the-fly algorthm called α-Dijk for path computation within a partition, which effectively prunes paths based on landmarks. Extensive experiments demonstrate that on continent-sized road networks, COLA answers an approximate CSP query in sub-second time, whereas existing methods take hours. Interestingly, even without an index, the α-Dijk algorithm in COLA still outperforms previous solutions by more than an order of magnitude. In the subgraph-freeness problem, we are given a constant-sized graph H, and wish to de- termine whether the network graph contains H as a subgraph or not. Until now, the only lower bounds on subgraph-freeness known for the CONGEST model were for cycles of length greater than 3; here we extend and generalize the cycle lower bound, and obtain polynomial lower bounds for subgraph-freeness in the CONGEST model for two classes of subgraphs. The first class contains any graph obtained by starting from a 2-connected graph H for which we already know a lower bound, and replacing the vertices of H by arbitrary connected graphs. We show that the lower bound on H carries over to the new graph. The second class is constructed by starting from a cycle Ck of length k ≥ 4, and constructing a graph H from Ck by replacing each edge i, (i + 1) mod k of the cycle with a connected graph Hi, subject to some constraints on the graphs H_ 0 , . . . , H_ k−1 . In this case we obtain a polynomial lower bound for the new graph H , depending on the size of the shortest cycle in H passing through the vertices of the original k-cycle. The popular h-index used to measure scientific output can be described in terms of a pool of evaluated objects (the papers), a quality function on the evaluated objects (the number of citations received by each paper) and a sentencing line crossing the origin, whose intersection with the graph of the quality function yields the index value (in the h-index this is a line with slope 1). Based on this abstraction, we present a new index, the c-index, in which the evaluated objects are the citations received by an author, a group of authors, a journal, etc., the quality function of a citation is the collaboration distance between the authors of the cited and the citing papers, and the sentencing line can take slopes between 0 and ∞. As a result, the new index counts only those citations which are significant enough, where significance is proportional to collaboration distance. Several advantages of the new c-index with respect to previous proposals are discussed. We study the problem of gathering at the same location two mobile agents that are dispersed in an unknown and unlabeled environment. This problem called Rendezvous, is a fundamental task in distributed coordination among autonomous entities. Most previous studies on the subject model the environment as an undirected graph and the solution techniques rely heavily on the fact that an agent can backtrack on any edge it traverses. However, such an assumption may not hold for certain scenarios, for instance a road network containing one-way streets. Thus, we consider the case of strongly connected directed graphs and present the first deterministic solution for rendezvous of two anonymous (identical) agents moving in such a digraph. Our algorithm achieves rendezvous with detection for any solvable instance of the problem, without any prior knowledge about the digraph, not even its size. For the classical minimum spanning tree problem we introduce disjunctive constraints for pairs of edges which can not be both included in the spanning tree at the same time. These constraints are represented by a conflict graph whose vertices correspond to the edges of the original graph. Edges in the conflict graph connect conflicting edges of the original graph. It is shown that the problem becomes strongly @math -hard even if the connected components of the conflict graph consist only of paths of length two. On the other hand, for conflict graphs consisting of disjoint edges (i.e. paths of length one) the problem remains polynomially solvable. We combine the known notion of the edge intersection graphs of paths in a tree with a VLSI grid layout model to introduce the edge intersection graphs of paths on a grid. Let P be a collection of nontrivial simple paths on a grid G. We define the edge intersection graph EPG(P) of P to have vertices which correspond to the members of P, such that two vertices are adjacent in EPG(P) if the corresponding paths in P share an edge in G. An undirected graph G is called an edge intersection graph of paths on a grid (EPG) if G = EPG(P) for some P and G, and 〈P,G〉 is an EPG representation of G. We prove that every graph is an EPG graph. A turn of a path at a grid point is called a bend. We consider here EPG representations in which every path has at most a single bend, called B1-EPG representations and the corresponding graphs are called B1-EPG graphs. We prove that any tree is a B1-EPG graph. Moreover, we give a structural property that enables one to generate non B1-EPG graphs. Furthermore, we characterize the representation of cliques and chordless 4-cycles in B1-EPG graphs. We also prove that single bend paths on a grid have Strong Helly number 3. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009 With the tremendous amount of research publications, recommending relevant papers to researchers to fulfill their information need becomes a significant problem. The major challenge to be tackled by our work is that given a target paper, how to effectively recommend a set of relevant papers from an existing citation network. In this paper, we propose a novel method to address the problem by incorporating various citation relations for a proper set of papers, which are more relevant but with a very limited size. The proposed method has two unique properties. Firstly, a metric called Local Relation Strength is defined to measure the dependency between cited and citing papers. Secondly, a model called Global Relation Strength is proposed to capture the relevance between two papers in the whole citation graph. We evaluate our proposed model on a real-world publication dataset and conduct an extensive comparison with the state-of-the-art baseline methods. The experimental results demonstrate that our method can have a promising improvement over the state-of-the-art techniques. Subgraph enumeration is important for many applications such as subgraph frequencies, network motif discovery, graphlet kernel computation, and studying the evolution of social networks. Most earlier work on subgraph enumeration assumes that graphs are resident in memory, which results in serious scalability problems. Recently, efforts to enumerate all subgraphs in a large-scale graph have seemed to enjoy some success by partitioning the data graph and exploiting the distributed frameworks such as MapReduce and distributed graph engines. However, we notice that all existing distributed approaches have serious performance problems for subgraph enumeration due to the explosive number of partial results. In this paper, we design and implement a disk-based, single machine parallel subgraph enumeration solution called DualSim that can handle massive graphs without maintaining exponential numbers of partial results. Specifically, we propose a novel concept of the dual approach for subgraph enumeration. The dual approach swaps the roles of the data graph and the query graph. Specifically, instead of fixing the matching order in the query and then matching data vertices, it fixes the data vertices by fixing a set of disk pages and then finds all subgraph matchings in these pages. This enables us to significantly reduce the number of disk reads. We conduct extensive experiments with various real-world graphs to systematically demonstrate the superiority of DualSim over state-of-the-art distributed subgraph enumeration methods. DualSim outperforms the state-of-the-art methods by up to orders of magnitude, while they fail for many queries due to explosive intermediate results. Let G = (V(G), E(G)) be a weighted directed graph and let P be a shortest path from s to t in G. In the replacement paths problem we are required to compute for every edge e in P, the length of a shortest path from s to t that avoids e. The fastest known algorithm for solving the problem in weighted directed graphs is the trivial one: each edge in P is removed from the graph in its turn and the distance from s to t in the modified graph is computed. The running time of this algorithm is O (mn + n2 log n), where n = |V(G)| and m = |E(G)|. The replacement paths problem is strongly motivated by two different applications. First, the fastest algorithm to compute the k simple shortest paths from s to t in directed graphs [21, 13] repeatedly computes the replacement paths from s to t. Its running time is O(kn(m + n log n)). Second, the computation of Vickrey pricing of edges in distributed networks can be reduced to the replacement paths problem. An open question raised by Nisan and Ronen [16] asks whether it is possible to compute the Vickrey pricing faster than the trivial algorithm described in the previous paragraph. In this paper we present a near-linear time algorithm for computing replacement paths in weighted planar directed graphs. In particular, the algorithm computes the lengths of the replacement paths in O(n log3 n) time. This result immediately improves the running time of the two applications mentioned above by almost a linear factor. Our algorithm is obtained by combining several new ideas with a data structure of Klein [12] that supports multi-source shortest paths queries in planar directed graphs in logarithmic time. Our algorithm can be adapted to address the variant of the problem in which one is interested in the replacement path itself (rather than the length of the path). In that case the algorithm is executed in a preprocessing stage constructing a data structure that supports replacement path queries in time O(h), where h is the number of hops in the replacement path. In addition, we can handle the variant in which vertices should be avoided instead of edges. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. Large graph databases are commonly collected and analyzed in numerous domains. For reasons related to either space efficiency or for privacy protection (e.g., in the case of social network graphs), it sometimes makes sense to replace the original graph with a summary, which removes certain details about the original graph topology. However, this summarization process leaves the database owner with the challenge of processing queries that are expressed in terms of the original graph, but are answered using the summary. In this paper, we propose a formal semantics for answering queries on summaries of graph structures. At its core, our formulation is based on a random worlds model. We show that important graph-structure queries (e.g., adjacency, degree, and eigenvector centrality) can be answered efficiently and in closed form using these semantics. Further, based on this approach to query answering, we formulate three novel graph partitioning compression problems. We develop algorithms for finding a graph summary that least affects the accuracy of query results, and we evaluate our proposed algorithms using both real and synthetic data. System area networks (SANs), which usually accept arbitrary topologies, have been used to connect hosts in PC clusters. Although deadlock-free routing is often employed for low-latency communications using wormhole or virtual cut-through switching, the interconnection adaptivity introduces difficulties in establishing deadlock-free paths. An up* down* routing algorithm, which has been widely used to avoid deadlocks in irregular networks, tends to make unbalanced paths as it employs a one-dimensional directed graph. The current study introduces a two-dimensional directed graph on which adaptive routings called left-up first turn (L-turn) routings and right-down last turn (R-turn) routings are proposed to make the paths as uniformly distributed as possible. This scheme guarantees deadlock-freedom because it uses the turn model approach, and the extra degree of freedom in the two-dimensional graph helps to ensure that the prohibited turns are well-distributed. Simulation results show that better throughput and latency results from uniformly distributing the prohibited turns by which the traffic would be more distributed toward the leaf nodes. The L-turn routings, which meet this condition, improve throughput by up to 100 percent compared with two up* down*-based routings, and also reduce latency