On dynamic shortest paths problems

Liam Roditty, Uri Zwick

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and dceremental singlesource shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs shortest-paths problem. We also obtain slightly weaker results for the corresponding unweighted problems. (ii) A randomized fully-dynamic algorithm for the all-pairs shortestpaths problem in directed unweighted graphs with an amortized update time of Õ(m√n) and a worst case query time is O(n3/4). (iii) A deterministic O(n2log n) time algorithm for constructing a (log n)-spanner with O(n) edges for any weighted undirected graph on n vertices. The algorithm uses a simple algorithm for incrementally maintaining single-source shortest-paths tree up to a given distance.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsSusanne Albers, Tomasz Radzik
PublisherSpringer Verlag
Pages580-591
Number of pages12
ISBN (Print)3540230254, 9783540230250
DOIs
StatePublished - 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3221
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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