A linear-size logarithmic stretch path-reporting distance oracle for general graphs

Michael Elkin, Seth Pettie

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

12 Scopus citations

Abstract

In a seminal paper [27] for any n-vertex undirected graph G=(V E) and a parameter k 1, 2,. Thorup and Zwick constructed a distance oracle of size 0 (kn1+1/k) which upon a query (u, v) constructs a path H between u and v of length δ (u, v) such that dG (n, v) ≤δ (u, v) ≤ (2k-1)dG (u, v). 'l'he query time of the oracle from [27] is O (k) (in addition to the length of the returned path), and it was subsequently improved to 0 (1) [29, 11]. A major drawback of the oracle of [27] is that its space is ω (n.·log vi). Mendel and Naor [18] devised an oracle with space O (n1+1/k) and stretch O (k), but their oracle can only report distance estimates and not actual paths. In this paper we devise a path-reporting distance oracle with size O (n1+1/k), stretch O (k) and query time O (nε), for an arbitrarily small ε > 0. In particular, for k=logn our oracle provides logarithmic stretch using linear size. Another variant of our oracle has linear size, polylogarithmic stretch, and query time O (1og log vi). For unweighted graphs we devise a distance oracle with multiplicative stretch O (1), additive stretch O (β (k)), for a function β, space O (n1+1/kk · β), and query time O (n), for an arbitrarily small constant ε> o T he tradeoff between multiplicative stretch and size in these oracles is far below Erdôs's girth conjecture threshold (which is stretch 2k-1 and size O (n1+1/kk)).

Original languageEnglish
Title of host publicationProceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
PublisherAssociation for Computing Machinery
Pages805-821
Number of pages17
EditionJanuary
ISBN (Electronic)9781611973747
DOIs
StatePublished - 1 Jan 2015
Event26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 - San Diego, United States
Duration: 4 Jan 20156 Jan 2015

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
NumberJanuary
Volume2015-January

Conference

Conference26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
Country/TerritoryUnited States
CitySan Diego
Period4/01/156/01/15

ASJC Scopus subject areas

  • Software
  • General Mathematics

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