SIAM Journal on Computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Journal of Algorithms
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Oracles for distances avoiding a link-failure
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Vickrey Prices and Shortest Paths: What is an Edge Worth?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A new approach to all-pairs shortest paths on real-weighted graphs
Theoretical Computer Science - Special issue on automata, languages and programming
Journal of the ACM (JACM)
All-pairs shortest paths for unweighted undirected graphs in o(mn) time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A near-linear time algorithm for computing replacement paths in planar directed graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Finding reliable subgraphs from large probabilistic graphs
Data Mining and Knowledge Discovery
Improved algorithms for the k simple shortest paths and the replacement paths problems
Information Processing Letters
A near-linear-time algorithm for computing replacement paths in planar directed graphs
ACM Transactions on Algorithms (TALG)
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Replacement paths and k simple shortest paths in unweighted directed graphs
ACM Transactions on Algorithms (TALG)
Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication
ACM Transactions on Algorithms (TALG)
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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 ε 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.