Nearly Optimal Fault Tolerant Distance Oracle

Dipan Dey; Manoj Gupta

Nearly Optimal Fault Tolerant Distance Oracle

Data Structures and Algorithms 2026-04-08 v8

Authors: Dipan Dey , Manoj Gupta

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 $O((cf \log (nW))^{O(f^2)})$ 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).

Keywords

fault tolerant distance oracle shortest path undirected weighted graph space complexity time complexity graph algorithms

Cite

@article{arxiv.2402.12832,
  title  = {Nearly Optimal Fault Tolerant Distance Oracle},
  author = {Dipan Dey and Manoj Gupta},
  journal= {arXiv preprint arXiv:2402.12832},
  year   = {2026}
}

Comments

We found the following error in the paper: in subcase (b) of case (III) of Section 9.3.1, we claimed that $se_k=su \odot ue_k$, which is not correct in some cases. For example, when $x$ and $e_k$ lie on different branches of $T_s$, it may be that in $T_x$, the path from $x$ to $e_k$ uses a different path that goes through $u$. However, the technical claims about the Jump Sequence are correct

Nearly Optimal Fault Tolerant Distance Oracle

Abstract

Keywords

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