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Approximate Shortest Paths Avoiding a Failed Vertex: Optimal Size Data Structures for Unweighted Graph
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 $t>1$: 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.
Cited literature [13 references]
https://hal.inria.fr/inria-00455747
Contributor : Publications Loria <>
Submitted on : Thursday, February 11, 2010 - 10:03:36 AM
Last modification on : Sunday, July 22, 2018 - 9:10:03 AM
Long-term archiving on: : Friday, June 18, 2010 - 8:09:41 PM
Contributor : Publications Loria <>
Submitted on : Thursday, February 11, 2010 - 10:03:36 AM
Last modification on : Sunday, July 22, 2018 - 9:10:03 AM
Long-term archiving on: : Friday, June 18, 2010 - 8:09:41 PM
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