In rendezvous, two agents traverse network edges in synchronous rounds and have to meet at some node. In treasure hunt, a single agent has to find a stationary target situated at an unknown node of the network. We study tradeoffs between the amount of information ( @math ) available @math to the agents and the cost (number of edge traversals) of rendezvous and treasure hunt. Our goal is to find the smallest size of advice which enables the agents to solve these tasks at some cost @math in a network with @math edges. This size turns out to depend on the initial distance @math and on the ratio @math , which is the @math due to advice. For arbitrary graphs, we give upper and lower bounds of @math and @math , respectively, on the optimal size of advice. For the class of trees, we give nearly tight upper and lower bounds of @math and @math , respectively.
Treasure hunt, network exploration and rendezvous in networks are interrelated problems that have received much attention in recent literature. Treasure hunt has been investigated in the line @cite_36 @cite_12 , in the plane @cite_50 and in other terrains @cite_30 . Treasure hunt in anonymous networks (without any information about the network) has been studied in @cite_48 @cite_31 with the goal of minimizing cost.
@cite_30 @cite_36 @cite_48 @cite_50 @cite_31 @cite_12
2085216434 1548168317 2623545498 2019729116 2949374709
In this paper, we investigate the explicit deterministic treasure hunt problem in a @math -vertex network. This problem was firstly introduced by Ta-Shma and Zwick in TZ07 [SODA'07]. Note also it is a variant of the well known rendezvous problem in which one of the robot (the treasure) is always stationary. In this paper, we propose an @math -time algorithm for the treasure hunt problem, which significantly improves the currently best known result of running time @math in TZ07 , where @math is a constant induced from the construction of an universal exploration sequence in R05,TZ07 , and @math is an arbitrary large, but fixed, integer constant. The treasure hunt problem also motivates the study of strongly universal exploration sequences. In this paper, we also propose a much better explicit construction for strongly universal exploration sequences compared to the one in TZ07 . We obtain several improved solutions for the deterministic rendezvous problem in general undirected graphs. Our solutions answer several problems left open in a recent paper by We also introduce an interesting variant of the rendezvous problem which we call the deterministic treasure hunt problem. Both the rendezvous and the treasure hunt problems motivate the study of universal traversal sequences and universal exploration sequences with some strengthened properties. We call such sequences strongly universal traversal (exploration) sequences. We give an explicit construction of strongly universal exploration sequences. The existence of strongly universal traversal sequences, as well as the solution of the most difficult variant of the deterministic treasure hunt problem, are left as intriguing open problems. In rendezvous, two agents traverse network edges in synchronous rounds and have to meet at some node. In treasure hunt, a single agent has to find a stationary target situated at an unknown node of the network. We study tradeoffs between the amount of information (advice) available a priori to the agents and the cost (number of edge traversals) of rendezvous and treasure hunt. Our goal is to find the smallest size of advice which enables the agents to solve these tasks at some cost C in a network with e edges. This size turns out to depend on the initial distance D and on the ratio e C , which is the relative cost gain due to advice. For arbitrary graphs, we give upper and lower bounds of O ( D log ( D ? e C ) + log log e ) and ? ( D log e C ) , respectively, on the optimal size of advice. For the class of trees, we give nearly tight upper and lower bounds of O ( D log e C + log log e ) and ? ( D log e C ) , respectively. In rendezvous, two agents traverse edges in rounds and have to meet at some node.In treasure hunt, an agent must find a fixed target at some node of the network.Objective: tradeoffs between the advice available to the agents and the cost.Results: bounds on the size of advice to achieve a given cost. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. 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.