Preprocess, Set, query!

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9 Scopus citations

Abstract

Thorup and Zwick [J. ACM and STOC'01] in their seminal work introduced the notion of distance oracles. Given an n-vertex weighted undirected graph with m edges, they show that for any integer k ≥ 1 it is possible to preprocess the graph in Õ (mm1/k) time and generate a compact data structure of size O(kn 1+1/k). For each pair of vertices, it is then possible to retrieve an estimated distance with multiplicative stretch 2k-1 in O(k) time. For k=2 this gives an oracle of O(n 1.5) size that produces in constant time estimated distances with stretch 3. Recently, Pǎtraşcu and Roditty [FOCS'10] broke the long-standing theoretical status-quo in the field of distance oracles and obtained a distance oracle for sparse unweighted graphs of O(n 5/3) size that produces in constant time estimated distances with stretch 2. In this paper we show that it is possible to break the stretch 2 barrier at the price of non-constant query time. We present a data structure that produces estimated distances with 1+ε stretch. The size of the data structure is O(nm 1-ε′) and the query time is Õ(m1-ε′). Using it for sparse unweighted graphs we can get a data structure of size O(n 1.86) that can supply in O(n 0.86) time estimated distances with multiplicative stretch 1.75.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2011 - 19th Annual European Symposium, Proceedings
Pages603-614
Number of pages12
DOIs
StatePublished - 2011
Event19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany
Duration: 5 Sep 20119 Sep 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6942 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th Annual European Symposium on Algorithms, ESA 2011
Country/TerritoryGermany
CitySaarbrucken
Period5/09/119/09/11

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