Near Optimal Dual Fault Tolerant Distance Oracle
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911939807936512 |
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| author | Dey, Dipan Gupta, Manoj |
| author_facet | Dey, Dipan Gupta, Manoj |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19709 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Near Optimal Dual Fault Tolerant Distance Oracle Dey, Dipan Gupta, Manoj Data Structures and Algorithms 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. |
| title | Near Optimal Dual Fault Tolerant Distance Oracle |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2406.19709 |