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
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
GRIN'01 No description on Graphics interface 2001
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
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
Many distances in planar graphs
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
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Probabilistic embeddings of bounded genus graphs into planar graphs
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Graph and map isomorphism and all polyhedral embeddings in linear time
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
An O(n log n) algorithm for maximum st-flow in a directed planar graph
Journal of the ACM (JACM)
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
Randomly removing g handles at once
Proceedings of the twenty-fifth annual symposium on Computational geometry
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Finding shortest contractible and shortest separating cycles in embedded graphs
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
Maximum flows and parametric shortest paths in planar graphs
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
Improved algorithms for min cut and max flow in undirected planar graphs
Proceedings of the forty-third annual ACM symposium on Theory of computing
Tightening Nonsimple Paths and Cycles on Surfaces
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
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Let G be a directed graph embedded on a surface of genus g. We describe an algorithm to compute the shortest non-separating cycle in G in O(g2 n log n) time, exactly matching the fastest algorithm known for undirected graphs. We also describe an algorithm to compute the shortest non-contractible cycle in G in gO(g)n log n time, matching the fastest algorithm for undirected graphs of constant genus.