Distance sensitivity oracles with subcubic preprocessing time and fast query time

Shiri Chechik, Sarel Cohen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present the first distance sensitivity oracle (DSO) with subcubic preprocessing time and poly-logarithmic query time for directed graphs with integer weights in the range [-M,M]. Weimann and Yuster [FOCS 10] presented a distance sensitivity oracle for a single vertex/edge failure with subcubic preprocessing time of O(Mnω+1-α) and subquadratic query time of Õ(n1+α), where α is any parameter in [0,1], n is the number of vertices, m is the number of edges, the Õ(·) notation hides poly-logarithmic factors in n and ω<2.373 is the matrix multiplication exponent. Later, Grandoni and Vassilevska Williams [FOCS 12] substantially improved the query time to sublinear in n. In particular, they presented a distance sensitivity oracle for a single vertex/edge failure with Õ(Mnω+1/2+ Mnω+α(4-ω)) preprocessing time and Õ(n1-α) query time. Despite the substantial improvement in the query time, it still remains polynomial in the size of the graph, which may be undesirable in many settings where the graph is of large scale. A natural question is whether one can hope for a distance sensitivity oracle with subcubic preprocessing time and very fast query time (of poly-logarithmic in n). In this paper we answer this question affirmatively by presenting a distance sensitive oracle supporting a single vertex/edge failure in subcubic Õ(Mn2.873) preprocessing time for ω=2.373, Õ(n2.5) space and near optimal query time of Õ(1). For comparison, with the same Õ(Mn2.873) preprocessing time the DSO of Grandoni and Vassilevska Williams has Õ(n0.693) query time. In fact, the best query time their algorithm can obtain is (Mn0.385) (with (Mn3) preprocessing time).

Original languageEnglish
Title of host publicationSTOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
EditorsKonstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, Julia Chuzhoy
Pages1375-1388
Number of pages14
ISBN (Electronic)9781450369794
DOIs
StatePublished - 8 Jun 2020
Event52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020 - Chicago, United States
Duration: 22 Jun 202026 Jun 2020

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing

Conference

Conference52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020
Country/TerritoryUnited States
CityChicago
Period22/06/2026/06/20

Keywords

  • Distance Sensitivity Oracles
  • Fault-Tolerant
  • Replacement Paths
  • Shortest Paths

All Science Journal Classification (ASJC) codes

  • Software

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