Approximate Distance Sensitivity Oracles in Subquadratic Space

Davide Bilò, Shiri Chechik, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, Simon Krogmann, Martin Schirneck

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

Abstract

An f-edge fault-tolerant distance sensitive oracle (f-DSO) with stretch σ ≥ 1 is a data structure that preprocesses a given undirected, unweighted graph G with n vertices and m edges, and a positive integer f. When queried with a pair of vertices s, t and a set F of at most f edges, it returns a σ-approximation of the s-t-distance in G-F. We study f-DSOs that take subquadratic space. Thorup and Zwick [JACM2015] showed that this is only possible for σ ≥ 3. We present, for any constant f ≥ 1 and α (0, 1/2), and any ϵ > 0, an f-DSO with stretch 3 + that takes O(n2-α/f+1/ϵ) · O(logn/ϵ)f+1 space and has an O(nα/ϵ2) query time. We also give an improved construction for graphs with diameter at most D. For any constant k, we devise an f-DSO with stretch 2k-1 that takes O(Df+o(1) n1+1/k) space and has O(Do(1)) query time, with a preprocessing time of O(Df+o(1) mn1/k). Chechik, Cohen, Fiat, and Kaplan [SODA 2017] presented an f-DSO with stretch 1+ and preprocessing time O(n5) · O(logn/ϵ)f, albeit with a super-quadratic space requirement. We show how to reduce their preprocessing time to O(mn2) · O(logn/ϵ)f.

Original languageEnglish
Title of host publicationSTOC 2023 - Proceedings of the 55th Annual ACM Symposium on Theory of Computing
EditorsBarna Saha, Rocco A. Servedio
PublisherAssociation for Computing Machinery
Pages1396-1409
Number of pages14
ISBN (Electronic)9781450399135
DOIs
StatePublished - 2 Jun 2023
Event55th Annual ACM Symposium on Theory of Computing, STOC 2023 - Orlando, United States
Duration: 20 Jun 202323 Jun 2023

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference55th Annual ACM Symposium on Theory of Computing, STOC 2023
Country/TerritoryUnited States
CityOrlando
Period20/06/2323/06/23

Keywords

  • approximate shortest paths
  • distance sensitivity oracle
  • fault-tolerant data structure
  • subquadratic space

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