Near Optimal Dual Fault Tolerant Distance Oracle
<|reference_start|>Near Optimal Dual Fault Tolerant Distance Oracle: 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.<|reference_end|>
@article{dey2024near,
    title={Near Optimal Dual Fault Tolerant Distance Oracle},
    author={Dipan Dey, Manoj Gupta},
    journal={arXiv preprint arXiv:2406.19709},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.19709},
    primaryClass={cs.DS}
}