Distributed Distance Sensitivity Oracles

Vignesh Manoharan; Vijaya Ramachandran

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arXiv · 2411.13728

Distributed Distance Sensitivity Oracles

Vignesh Manoharan·Vijaya Ramachandran

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Abstract

We present results for the distance sensitivity oracle (DSO) problem, where one needs to preprocess a given directed weighted graph $G=(V,E)$ in order to answer queries about the shortest path distance in $G$ from vertex $s$ to vertex $t$ avoiding edge $e$, for any $s,t \in V, e \in E$. DSO enables optimal re-routing under a link failure, and can serve as a key component for fault tolerance in a distributed setting. However, no non-trivial results for DSO are known in the distributed CONGEST model. We present DSO algorithms with different tradeoffs between preprocessing and query cost: one that optimizes query response rounds, and another that prioritizes preprocessing rounds. We complement these algorithms with unconditional CONGEST lower bounds for DSO. Our DSO lower bounds build on a lower bound we present for the $k$-source shortest paths problem ($k$-SSP), which may be of independent interest. Additionally, we present almost-optimal upper and lower bounds for the related all pairs second simple shortest path (2-APSiSP) problem.

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BibTeX RIS

Vignesh Manoharan, Vijaya Ramachandran. 2025-11-12. Distributed Distance Sensitivity Oracles. https://arxiv.org/abs/2411.13728

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