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Compact and Fast Sensitivity Oracles for Single-Source Distances

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Abstract

Let s denote a distinguished source vertex of a non-negatively real weighted and undirected graph G with n vertices and m edges. In this paper we present two efficient single-source approximate-distance sensitivity oracles, namely compact data structures which are able to quickly report an approximate (by a multiplicative stretch factor) distance from s to any node of G following the failure of any edge in G. More precisely, we first present a sensitivity oracle of size O(n) which is able to report 2-approximate distances from the source in O(1) time. Then, we further develop our construction by building, for any 0<epsilon<1, another sensitivity oracle having size O(n*1/epsilon*log(1/epsilon)), and is able to report a (1+epsilon)-approximate distance from s to any vertex of G in O(log(n)*1/epsilon*log(1/epsilon)) time. Thus, this latter oracle is essentially optimal as far as size and stretch are concerned, and it only asks for a logarithmic query time. Finally, our results are complemented with a space lower bound for the related class of single-source additively-stretched sensitivity oracles, which is helpful to realize the hardness of designing compact oracles of this type.

BibTeX - Entry

@InProceedings{bilo_et_al:LIPIcs:2016:6364,
  author =	{Davide Bilo and Luciano Guala and Stefano Leucci and Guido Proietti},
  title =	{{Compact and Fast Sensitivity Oracles for Single-Source Distances}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6364},
  URN =		{urn:nbn:de:0030-drops-63640},
  doi =		{10.4230/LIPIcs.ESA.2016.13},
  annote =	{Keywords: fault-tolerant shortest-path tree, approximate distance, distance sensitivity oracle}
}

Keywords: fault-tolerant shortest-path tree, approximate distance, distance sensitivity oracle
Seminar: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue date: 2016
Date of publication: 2016


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