On the k-simple shortest paths problem in weighted directed graphs

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Abstract

We obtain the first approximation algorithm for finding the k-simple shortest paths connecting a pair of vertices in a weighted directed graph. Our algorithm is deterministic and has a running time of O(k(m√n + n3/2 log n)), where m is the number of edges in the graph and n is the number of vertices. Let s, t ∈ V; the length of the i-th simple path from s to t computed by our algorithm is at most 3/2 times the length of the i-th shortest simple path from s to t. The best algorithms for computing the exact k-simple shortest paths connecting a pair of vertices in a weighted directed graph are due to Yen [19] and Lawler [13]. The running time of their algorithms, using modern data structures, is O(k(mn+n2 log n)). Both algorithms are from the early 70's. Although this problem and other variants of the k-shortest path problem drew a lot of attention during the last three and a half decades, the O(k(mn + n2 log n)) bound is still unbeaten.

Original languageEnglish
Title of host publicationProceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007
PublisherAssociation for Computing Machinery
Pages920-928
Number of pages9
ISBN (Electronic)9780898716245
StatePublished - 2007
Externally publishedYes
Event18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007 - New Orleans, United States
Duration: 7 Jan 20079 Jan 2007

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume07-09-January-2007

Conference

Conference18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007
Country/TerritoryUnited States
CityNew Orleans
Period7/01/079/01/07

Bibliographical note

Publisher Copyright:
Copyright © 2007 by the Association for Computing Machinery, Inc. and the Society for Industrial and Applied Mathematics.

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