Maximum (s,t)-flows in planar networks in O(|V| log |V|) time
Journal of Computer and System Sciences
A faster computation of the most vital edge of a shortest path
Information Processing Letters
Oracles for distances avoiding a link-failure
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On the Difficulty of Some Shortest Path Problems
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth 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
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
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third 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
Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication
ACM Transactions on Algorithms (TALG)
Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
Linear-time algorithms for max flow and multiple-source shortest paths in unit-weight planar graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P, the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linear-space algorithm with O(n log n) running time for n-vertex planar directed graphs. The previous best time bound was O(n log2 n).