Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
A data structure for dynamic trees
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Finding minimum-cost circulations by canceling negative cycles
Journal of the ACM (JACM)
Strongly polynomial-time and NC algorithms for detecting cycles in periodic graphs
Journal of the ACM (JACM)
The lattice structure of flow in planar graphs
SIAM Journal on Discrete Mathematics
Flow in Planar Graphs with Multiple Sources and Sinks
SIAM Journal on Computing
Edge-disjoint (s,t)-paths in undirected planar graphs in linear time
Journal of Algorithms
Faster shortest-path algorithms for planar graphs
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Maximum (s,t)-flows in planar networks in O(|V| log |V|) time
Journal of Computer and System Sciences
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
An Efficient Multi-Dimensional Searching Technique and itsApplications
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The complexity of some problems in parametric linear and combinatorial programming
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Algorithms for network flows
Dynamizing static algorithms, with applications to dynamic trees and history independence
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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Maintaining information in fully dynamic trees with top trees
ACM Transactions on Algorithms (TALG)
Planar graphs, negative weight edges, shortest paths, and near linear time
Journal of Computer and System Sciences - Special issue on FOCS 2001
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Partition of planar flow networks
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Exploiting planarity for network flow and connectivity problems
Exploiting planarity for network flow and connectivity problems
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
An O(n log n) algorithm for maximum st-flow in a directed planar graph
Journal of the ACM (JACM)
Discrete Applied Mathematics
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Finding shortest non-trivial cycles in directed graphs on surfaces
Proceedings of the twenty-sixth annual symposium on Computational geometry
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Computing the girth of a planar graph in linear time
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Shortest path based planar graph cuts for bi-layer segmentation of binocular stereo video
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
On the complexity of time-dependent shortest paths
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Minimum cuts and shortest non-separating cycles via homology covers
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
Contraction network for solving maximum flow problem
Proceedings of the ACM SIGKDD Workshop on Mining Data Semantics
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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We observe that the classical maximum flow problem in any directed planar graph G can be reformulated as a parametric shortest path problem in the oriented dual graph G*. This reformulation immediately suggests an algorithm to compute maximum flows, which runs in O(n log n) time. As we continuously increase the parameter, each change in the shortest path tree can be effected in O(log n) time using standard dynamic tree data structures, and the special structure of the parametrization implies that each directed edge enters the evolving shortest path tree at most once. The resulting maximum-flow algorithm is identical to the recent algorithm of Borradaile and Klein [J. ACM 2009], but our new formulation allows a simpler presentation and analysis. On the other hand, we demonstrate that for a similarly structured parametric shortest path problem on the torus, the shortest path tree can change Ω(n2) times in the worst case, suggesting that a different method may be required to efficiently compute maximum flows in higher-genus graphs.