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Efficient Algorithms for Shortest Paths in Sparse Networks

Efficient Algorithms for Shortest Paths in Sparse Networks Algorithms for finding shortest paths are presented which are faster than algorithms previously known on networks which are relatively sparse in arcs. Known results which the results of this paper extend are surveyed briefly and analyzed. A new implementation for priority queues is employed, and a class of “arc set partition” algorithms is introduced. For the single source problem on networks with nonnegative arcs a running time of O (min( n 1+1/ k + e , n + e ) log n )) is achieved, where there are n nodes and e arcs, and k is a fixed integer satisfying k > 0. This bound is O ( e ) on dense networks. For the single source and all pairs problem on unrestricted networks the running time is O (min( n 2+1/ k + ne , n 2 log n + ne log n ). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

Efficient Algorithms for Shortest Paths in Sparse Networks

Johnson, Donald B.
Journal of the ACM (JACM) , Volume 24 (1) – Jan 1, 1977
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Publisher
Association for Computing Machinery
Copyright
The ACM Portal is published by the Association for Computing Machinery. Copyright © 2010 ACM, Inc.
Subject
Network problems
ISSN
0004-5411
DOI
10.1145/321992.321993
Publisher site
See Article on Publisher Site

Abstract

Algorithms for finding shortest paths are presented which are faster than algorithms previously known on networks which are relatively sparse in arcs. Known results which the results of this paper extend are surveyed briefly and analyzed. A new implementation for priority queues is employed, and a class of “arc set partition” algorithms is introduced. For the single source problem on networks with nonnegative arcs a running time of O (min( n 1+1/ k + e , n + e ) log n )) is achieved, where there are n nodes and e arcs, and k is a fixed integer satisfying k > 0. This bound is O ( e ) on dense networks. For the single source and all pairs problem on unrestricted networks the running time is O (min( n 2+1/ k + ne , n 2 log n + ne log n ).

Journal

Journal of the ACM (JACM) – Association for Computing Machinery

Published: Jan 1, 1977

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