TY - JOUR

T1 - On the k-simple shortest paths problem in weighted directed graphs

AU - Roditty, Liam

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Copyright © 2007 by the Association for Computing Machinery, Inc. and the Society for Industrial and Applied Mathematics. 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84969235544&partnerID=8YFLogxK

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VL - 07-09-January-2007

JO - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

JF - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

ER -