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

Authors Neelesh Khanna, Surender Baswana

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Keywords
  • Shortest path
  • distance
  • distance queries
  • oracle

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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.

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Neelesh Khanna and Surender Baswana. Approximate Shortest Paths Avoiding a Failed Vertex: Optimal Size Data Structures for Unweighted Graphs. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 513-524, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010) https://doi.org/10.4230/LIPIcs.STACS.2010.2481

Author Details

Neelesh Khanna
Surender Baswana
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