A separator theorem for graphs of bounded genus
Journal of Algorithms
Topological graph theory
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A data structure for dynamic trees
Journal of Computer and System Sciences
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Using separation algorithms in fixed dimension
Journal of Algorithms
Strongly polynomial-time and NC algorithms for detecting cycles in periodic graphs
Journal of the ACM (JACM)
A faster strongly polynomial minimum cost flow algorithm
Operations Research
Fast and efficient parallel solution of sparse linear systems
SIAM Journal on Computing
Flow in Planar Graphs with Multiple Sources and Sinks
SIAM Journal on Computing
Weighted Multidimensional Search and itsApplication to Convex Optimization
SIAM Journal on Computing
Linear Algorithms for Partitioning Embedded Graphs of BoundedGenus
SIAM Journal on Discrete Mathematics
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
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Isomorphism testing for embeddable graphs through definability
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient Sequential and Parallel Algorithms for Planar Minimum Cost Flow
SIGAL '90 Proceedings of the International Symposium on Algorithms
Planarization of Graphs Embedded on Surfaces
WG '95 Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
An Efficient Multi-Dimensional Searching Technique and itsApplications
An Efficient Multi-Dimensional Searching Technique and itsApplications
Algorithms for network flows
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
An O (n log n) algorithm for maximum st-flow in a directed planar graph
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
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
Approximation algorithms via contraction decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Maximum s-t-flow with k crossings in O(k3n log n) time
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A polynomial-time approximation scheme for Steiner tree in planar graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster approximate lossy generalized flow via interior point algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
Partition of planar flow networks
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Speeding-up linear programming using fast matrix multiplication
SFCS '89 Proceedings of the 30th 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
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
ε-Approximation minimization of convex functions in fixed dimension
Operations Research Letters
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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
Approximating loops in a shortest homology basis from point data
Proceedings of the twenty-sixth annual symposium on Computational geometry
Maximum flows and parametric shortest paths in planar graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Hardness results for homology localization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Shortest cut graph of a surface with prescribed vertex set
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Shortest paths in planar graphs with real lengths in O(n log2n/ log log n) time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third 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
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 describe the first algorithms to compute maximum flows in surface-embedded graphs in near-linear time. Specifically, given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, we can compute a maximum (s,t)-flow in O(g7 n log2 n log2 C) time for integer capacities that sum to C, or in (g log n)O(g) n time for real capacities. Except for the special case of planar graphs, for which an O(n log n)-time algorithm has been known for 20 years, the best previous time bounds for maximum flows in surface-embedded graphs follow from algorithms for general sparse graphs. Our key insight is to optimize the relative homology class of the flow, rather than directly optimizing the flow itself. A dual formulation of our algorithm computes the minimum-cost cycle or circulation in a given (real or integer) homology class.