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Approximate Shortest Paths Avoiding a Failed Vertex: Optimal Size Data Structures for Unweighted Graphs

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Abstract

Let $G=(V,E)$ be any undirected graph on $V$ vertices and $E$ edges. A path $\textbf{P}$ between any two vertices $u,v\in V$ is said to be $t$-approximate shortest path if its length is at most $t$ times the length of the shortest path between $u$ and $v$. We consider the problem of building a compact data structure for a given graph $G$ which is capable of answering the following query for any $u,v,z\in V$ and $t>1$. \centerline{\em report $t$-approximate shortest path between $u$ and $v$ when vertex $z$ fails} We present data structures for the single source as well all-pairs versions of this problem. Our data structures guarantee optimal query time. Most impressive feature of our data structures is that their size {\em nearly} match the size of their best static counterparts.

BibTeX - Entry

@InProceedings{khanna_et_al:LIPIcs:2010:2481,
  author =	{Neelesh Khanna and Surender Baswana},
  title =	{{Approximate Shortest Paths Avoiding a Failed Vertex: Optimal Size Data Structures for Unweighted Graphs}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{513--524},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2481},
  URN =		{urn:nbn:de:0030-drops-24812},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2010.2481},
  annote =	{Keywords: Shortest path, distance, distance queries, oracle}
}

Keywords: Shortest path, distance, distance queries, oracle
Seminar: 27th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2010
Date of publication: 2010


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