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arXiv · 2406.19709

Near Optimal Dual Fault Tolerant Distance Oracle

Dipan Dey·Manoj Gupta
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Abstract

We present a dual fault-tolerant distance oracle for undirected and unweighted graphs. Given a set $F$ of two edges, as well as a source node $s$ and a destination node $t$, our oracle returns the length of the shortest path from $s$ to $t$ that avoids $F$ in $O(1)$ time with a high probability. The space complexity of our oracle is $\Tilde{O}(n^2)$ \footnote{$\Tilde{O}$ hides poly$\log n$ factor }, making it nearly optimal in terms of both space and query time. Prior to our work, Pettie and Duan [SODA 2009] designed a dual fault-tolerant distance oracle that required $\Tilde{O}(n^2)$ space and $O(\log n)$ query time. In addition to improving the query time, our oracle is much simpler than the previous approach.

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Dipan Dey, Manoj Gupta. 2024-06-28. Near Optimal Dual Fault Tolerant Distance Oracle. https://arxiv.org/abs/2406.19709

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