MPVX15 devised a distributed They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in MPVX15 . algorithm in the CONGEST model, that given a parameter @math , constructs an @math -spanner of an input unweighted @math -vertex graph with @math expected edges in @math rounds of communication. In this paper we improve the result of MPVX15 , by showing a @math -round distributed algorithm in the same model, that constructs a @math -spanner with @math edges, with probability @math , for any @math . Moreover, when @math , our algorithm produces (still in @math rounds) ultra-sparse spanners, i.e., spanners of size @math , with probability @math . To our knowledge, this is the first distributed algorithm in the CONGEST or in the PRAM models that constructs spanners or skeletons (i.e., connected spanning subgraphs) that sparse. Our algorithm can also be implemented in linear time in the standard centralized model, and for large @math , it provides spanners that are sparser than any other spanner given by a known (near-)linear time algorithm. We also devise improved bounds (and algorithms realizing these bounds) for @math -spanners and emulators. In particular, we show that for any unweighted @math -vertex graph and any @math , there exists a @math -emulator with @math edges. All previous constructions of @math -spanners and emulators employ a superlinear number of edges, for all choices of parameters. Finally, we provide some applications of our results to approximate shortest paths' computation in unweighted graphs.
Efficient algorithms for constructing @math -spanners were also devised in @cite_50 @cite_43 @cite_47 @cite_35 @cite_24 . These algorithms are based, however, on different approaches than that of the current paper. The latter is based on @cite_6 . Specifically, the approach of @cite_50 @cite_43 is based on @cite_21 @cite_28 construction of pairwise covers and hopsets, i.e., the algorithm works top-down. It recurses in small clusters, and eliminates large ones. The approach of @cite_47 @cite_35 @cite_24 is based on @cite_61 collection of trees, used originally for distance oracles. Streaming algorithms for constructing multiplicative spanners were given in @cite_9 @cite_27 @cite_16 , and near-additive spanners in @cite_50 @cite_43 . Spanners and emulators with sublinear error were given in @cite_47 @cite_35 . Spanners with purely additive error and lower bounds concerning them were given in @cite_7 @cite_6 @cite_12 @cite_3 @cite_52 @cite_26 @cite_1 @cite_8 .
@cite_35 @cite_3 @cite_43 @cite_8 @cite_21 @cite_52 @cite_26 @cite_7 @cite_28 @cite_6 @cite_27 @cite_50 @cite_16 @cite_12 @cite_61 @cite_9 @cite_1 @cite_24 @cite_47
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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 . A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. 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. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ...