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Nearly Optimal Fault Tolerant Distance Oracle (2402.12832v7)

Published 20 Feb 2024 in cs.DS

Abstract: We present an $f$-fault tolerant distance oracle for an undirected weighted graph where each edge has an integral weight from $[1 \dots W]$. Given a set $F$ of $f$ edges, as well as a source node $s$ and a destination node $t$, our oracle returns the \emph{shortest path} from $s$ to $t$ avoiding $F$ in $O((cf \log (nW)){O(f2)})$ time, where $c > 1$ is a constant. The space complexity of our oracle is $O(f4n2\log2 (nW))$. For a constant $f$, our oracle is nearly optimal both in terms of space and time (barring some logarithmic factor).

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