Nearly Optimal Fault Tolerant Distance Oracle
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917386862460928 |
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| author | Dey, Dipan Gupta, Manoj |
| author_facet | Dey, Dipan Gupta, Manoj |
| contents | 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 $O((cf \log (nW))^{O(f^2)})$ time, where $c > 1$ is a constant. The space complexity of our oracle is $O(f^4n^2\log^2 (nW))$. For a constant $f$, our oracle is nearly optimal both in terms of space and time (barring some logarithmic factor). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12832 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nearly Optimal Fault Tolerant Distance Oracle Dey, Dipan Gupta, Manoj Data Structures and Algorithms 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 $O((cf \log (nW))^{O(f^2)})$ time, where $c > 1$ is a constant. The space complexity of our oracle is $O(f^4n^2\log^2 (nW))$. For a constant $f$, our oracle is nearly optimal both in terms of space and time (barring some logarithmic factor). |
| title | Nearly Optimal Fault Tolerant Distance Oracle |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2402.12832 |