文章基本信息

标题：Additive Spanners and Distance Oracles in Quadratic Time
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作者：Mathias Bæk Tejs Knudsen
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：80
页码：64:1-64:12
DOI：10.4230/LIPIcs.ICALP.2017.64
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Let G be an unweighted, undirected graph. An additive k-spanner of G is a subgraph H that approximates all distances between pairs of nodes up to an additive error of +k, that is, it satisfies d_H(u,v) <= d_G(u,v)+k for all nodes u,v, where d is the shortest path distance. We give a deterministic algorithm that constructs an additive O(1)-spanner with O(n^(4/3)) edges in O(n^2) time. This should be compared with the randomized Monte Carlo algorithm by Woodruff [ICALP 2010] giving an additive 6-spanner with O(n^(4/3)log^3 n) edges in expected time O(n^2 log^2 n). An (alpha,beta)-approximate distance oracle for G is a data structure that supports the following distance queries between pairs of nodes in G. Given two nodes u, v it can in constant time compute a distance estimate d' that satisfies d <= d' <= alpha d + beta where d is the distance between u and v in G. Sommer [ICALP 2016] gave a randomized Monte Carlo (2,1)-distance oracle of size O(n^(5/3) polylog n) in expected time O(n^2 polylog n). As an application of the additive O(1)-spanner we improve the construction by Sommer [ICALP 2016] and give a Las Vegas (2,1)-distance oracle of size O(n^(5/3)) in time O(n^2). This also implies an algorithm that in O(n^2) time gives approximate distance for all pairs of nodes in G improving on the O(n^2 log n) algorithm by Baswana and Kavitha [SICOMP 2010].
关键词：graph algorithms; data structures; additive spanners; distance oracles