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.
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Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.513-524, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science
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Neelesh Khanna, Surender Baswana. Approximate Shortest Paths Avoiding a Failed Vertex: Optimal Size Data Structures for Unweighted Graph. Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.513-524, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science. <inria-00455747>

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