Approximate Shortest Paths Avoiding a Failed Vertex: Optimal Size Data Structures for Unweighted Graphs
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.
Shortest path
distance
distance queries
oracle
513-524
Regular Paper
Neelesh
Khanna
Neelesh Khanna
Surender
Baswana
Surender Baswana
10.4230/LIPIcs.STACS.2010.2481
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