Matching is as easy as matrix inversion
Combinatorica
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
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
Minimum cuts in near-linear time
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
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
A deterministic near-linear time algorithm for finding minimum cuts in planar graphs
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
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
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
A polynomial-time approximation scheme for Steiner tree in planar graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On Computing Handle and Tunnel Loops
CW '07 Proceedings of the 2007 International Conference on Cyberworlds
Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
Exploiting planarity for network flow and connectivity problems
Exploiting planarity for network flow and connectivity problems
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
Measuring and computing natural generators for homology groups
Computational Geometry: Theory and Applications
Finding shortest contractible and shortest separating cycles in embedded graphs
ACM Transactions on Algorithms (TALG)
ACM Transactions on Algorithms (TALG)
Output-sensitive algorithm for the edge-width of an embedded graph
Proceedings of the twenty-sixth 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
ACM Transactions on Algorithms (TALG)
Computing the Shortest Essential Cycle
Discrete & Computational Geometry
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
Hardness results for homology localization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Improved algorithms for min cut and max flow in undirected planar graphs
Proceedings of the forty-third annual ACM symposium on Theory of computing
The least spanning area of a knot and the optimal bounding chain problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Min-cuts and shortest cycles in planar graphs in O(n log log n) time
ESA'11 Proceedings of the 19th European conference on Algorithms
Tightening Nonsimple Paths and Cycles on Surfaces
SIAM Journal on Computing
Optimal Homologous Cycles, Total Unimodularity, and Linear Programming
SIAM Journal on Computing
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
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
Structured recursive separator decompositions for planar graphs in linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
We give a deterministic algorithm to find the minimum cut in a surface-embedded graph in near-linear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut in gO(g)n log log n time, matching the running time of the fastest algorithm known for planar graphs, due to Łacki and Sankowski, for any constant g. Indeed, our algorithm calls Łacki and Sankowski's recent O(n log log n) time planar algorithm as a subroutine. Previously, the best time bounds known for this problem followed from two algorithms for general sparse graphs: a randomized algorithm of Karger that runs in O(n log3 n) time and succeeds with high probability, and a deterministic algorithm of Nagamochi and Ibaraki that runs in O(n2 log n) time. We can also achieve a deterministic gO(g)n2 log log n time bound by repeatedly applying the best known algorithm for minimum (s, t)-cuts in surface graphs. The bulk of our work focuses on the case where the dual of the minimum cut splits the underlying surface into multiple components with positive genus.