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.2019.12
URN: urn:nbn:de:0030-drops-115087
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11508/
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Jain, Rahul ; Tewari, Raghunath

Reachability in High Treewidth Graphs

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LIPIcs-ISAAC-2019-12.pdf (0.5 MB)

Abstract

Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability; however, their space complexity is also linear. On the other hand, Savitch's algorithm takes quasipolynomial time although the space bound is O(log^2 n). Here, we study space efficient algorithms for deciding reachability that run in polynomial time.
In this paper, we show that given an n vertex directed graph of treewidth w along with its tree decomposition, there exists an algorithm running in polynomial time and O(w log n) space that solves the reachability problem.

BibTeX - Entry

@InProceedings{jain_et_al:LIPIcs:2019:11508,
  author =	{Rahul Jain and Raghunath Tewari},
  title =	{{Reachability in High Treewidth Graphs}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11508},
  URN =		{urn:nbn:de:0030-drops-115087},
  doi =		{10.4230/LIPIcs.ISAAC.2019.12},
  annote =	{Keywords: graph reachability, simultaneous time-space upper bound, tree decomposition}
}

Keywords: graph reachability, simultaneous time-space upper bound, tree decomposition
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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