文章基本信息

标题：Brief Announcement: A Centralized Local Algorithm for the Sparse Spanning Graph Problem
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作者：Christoph Lenzen ; Reut Levi
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：91
页码：57:1-57:3
DOI：10.4230/LIPIcs.DISC.2017.57
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by examining only a small part of the input; yet, answers must be globally consistent and independent of prior queries. Unfortunately, maximally sparse spanning subgraphs, i.e., spanning trees, cannot be constructed efficiently in this model. Therefore, we settle for a spanning subgraph containing at most (1+epsilon)n edges (where n is the number of vertices and epsilon is a given approximation/sparsity parameter). We achieve a query complexity of O(poly(Delta/epsilon)n^(2/3)) (up to polylogarithmic factors in n) where Delta is the maximum degree of the input graph. Our algorithm is the first to do so on arbitrary bounded degree graphs. Moreover, we achieve the additional property that our algorithm outputs a spanner, i.e., distances are approximately preserved. With high probability, for each deleted edge there is a path of O(log n (Delta+log n)/epsilon) hops in the output that connects its endpoints.
关键词：local; spanning graph; sparse