License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2018.56
URN: urn:nbn:de:0030-drops-100042
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10004/
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Bezáková, Ivona ; Searns, Andrew

On Counting Oracles for Path Problems

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LIPIcs-ISAAC-2018-56.pdf (0.4 MB)

Abstract

We initiate the study of counting oracles for various path problems in graphs. Distance oracles have gained a lot of attention in recent years, with studies of the underlying space and time tradeoffs. For a given graph G, a distance oracle is a data structure which can be used to answer distance queries for pairs of vertices s,t in V(G). In this work, we extend the set up to answering counting queries: for a pair of vertices s,t, the oracle needs to provide the number of (shortest or all) paths from s to t. We present O(n^{1.5}) preprocessing time, O(n^{1.5}) space, and O(sqrt{n}) query time algorithms for oracles counting shortest paths in planar graphs and for counting all paths in planar directed acyclic graphs. We extend our results to other graphs which admit small balanced separators and present applications where our oracle improves the currently best known running times.

BibTeX - Entry

@InProceedings{bezkov_et_al:LIPIcs:2018:10004,
  author =	{Ivona Bez{\'a}kov{\'a} and Andrew Searns},
  title =	{{On Counting Oracles for Path Problems}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{56:1--56:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10004},
  URN =		{urn:nbn:de:0030-drops-100042},
  doi =		{10.4230/LIPIcs.ISAAC.2018.56},
  annote =	{Keywords: Counting oracle, Path problems, Shortest paths, Separators}
}

Keywords: Counting oracle, Path problems, Shortest paths, Separators
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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