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

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* Corresponding author 1 Oracle India Pvt. Ltd 2 Indian Institute of Technology

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.

Mots-clés : Shortest path distance distance queries oracle

Autor: Neelesh Khanna - Surender Baswana -

Fuente: https://hal.archives-ouvertes.fr/

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