High probability parallel transitive-closure algorithms
SIAM Journal on Computing
Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
SIAM Journal on Computing
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
A faster computation of the most vital edge of a shortest path
Information Processing Letters
Improved decremental algorithms for maintaining transitive closure and all-pairs shortest paths
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Oracles for distances avoiding a link-failure
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
All pairs shortest paths using bridging sets and rectangular matrix multiplication
Journal of the ACM (JACM)
Maintaining all-pairs approximate shortest paths under deletion of edges
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Erratum to "Vickrey Pricing and Shortest Paths: What is an Edge Worth?"
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the Difficulty of Some Shortest Path Problems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Fully dynamic biconnectivity and transitive closure
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Vickrey Prices and Shortest Paths: What is an Edge Worth?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Dynamic Approximate All-Pairs Shortest Paths in Undirected Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On the K-simple shortest paths problem in weighted directed graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A near-linear time algorithm for computing replacement paths in planar directed graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Dual-failure distance and connectivity oracles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Improved algorithms for the k simple shortest paths and the replacement paths problems
Information Processing Letters
A nearly optimal oracle for avoiding failed vertices and edges
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Solving the replacement paths problem for planar directed graphs in O(n log n) time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the $k$ Shortest Simple Paths Problem in Weighted Directed Graphs
SIAM Journal on Computing
An experimental study on approximating K shortest simple paths
ESA'11 Proceedings of the 19th European conference on Algorithms
Efficient associative algorithm for finding the second simple shortest paths in a digraph
PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
Single source distance oracle for planar digraphs avoiding a failed node or link
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Computing replacement paths in surface embedded graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Finding Alternative Shortest Paths in Spatial Networks
ACM Transactions on Database Systems (TODS)
Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication
ACM Transactions on Algorithms (TALG)
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Let G=(V,E) be a directed graph and let P be a shortest path from s to t in G. In the replacement paths problem we are required to find, for every edge e on P, a shortest path from s to t in G that avoids e. We present the first non-trivial algorithm for computing replacement paths in unweighted directed graphs (and in graphs with small integer weights). Our algorithm is Monte-Carlo and its running time is ${\tilde O}(m\sqrt{n})$. Using the improved algorithm for the replacement paths problem we get an improved algorithm for finding the ksimple shortest paths between two given vertices.