Nearly Optimal Approximate Dual-Failure Replacement Paths

Shiri Chechik, Tianyi Zhang

Research output: Contribution to conferencePaperpeer-review

Abstract

Given a directed graph G = (V, E, ω) on n vertices with positive edge weights as well as two designated terminals s, t ∈ V, our goal is to compute the shortest path from s to t avoiding any pair of presumably failed edges f1, f2 ∈ E, which is a natural generalization of the classical replacement path problem which considers single edge failures only. This dual failure replacement paths problem was recently studied by [Vassilevska Williams, Woldeghebriela and Xu, 2022] who designed a O(n3) time algorithm for general weighted digraphs which is conditionally optimal. In the same paper, they also showed that the cubic time barrier can be bypassed by a O(M2/3n2.9146) time algorithm for input graphs with small integer edge weights from {−M, −M + 1, · · ·, M − 1, M}. In this paper, we study the natural question whether sub-cubic time algorithms exist for general weighted digraphs when approximation is allowed. As our main result, we show that (1 + є)-approximations of all dual-failure replacement paths can be computed in O∊(n2) time which is nearly optimal.

Original languageEnglish
Pages2568-2596
Number of pages29
DOIs
StatePublished - 2024
Event35th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2024 - Alexandria, United States
Duration: 7 Jan 202410 Jan 2024

Conference

Conference35th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2024
Country/TerritoryUnited States
CityAlexandria
Period7/01/2410/01/24

All Science Journal Classification (ASJC) codes

  • Software
  • General Mathematics

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