License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ICALP.2017.64
URN: urn:nbn:de:0030-drops-73924
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7392/
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Knudsen, Mathias Bæk Tejs

Additive Spanners and Distance Oracles in Quadratic Time

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LIPIcs-ICALP-2017-64.pdf (0.5 MB)

Abstract

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].

BibTeX - Entry

@InProceedings{knudsen:LIPIcs:2017:7392,
  author =	{Mathias Bæk Tejs Knudsen},
  title =	{{Additive Spanners and Distance Oracles in Quadratic Time}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{64:1--64:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7392},
  URN =		{urn:nbn:de:0030-drops-73924},
  doi =		{10.4230/LIPIcs.ICALP.2017.64},
  annote =	{Keywords: graph algorithms, data structures, additive spanners, distance oracles}
}

Keywords: graph algorithms, data structures, additive spanners, distance oracles
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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