Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Proceedings of the nineteenth 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
Testing contractibility in planar rips complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
Schnyder woods for higher genus triangulated surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Coloring triangle-free graphs on surfaces
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Finding shortest contractible and shortest separating cycles in embedded graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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)
Approximating the crossing number of toroidal graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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)
Dynamic programming for graphs on surfaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Shortest cut graph of a surface with prescribed vertex set
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
Tightening Nonsimple Paths and Cycles on Surfaces
SIAM Journal on Computing
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Shortest non-crossing walks in the plane
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
Algorithms for the edge-width of an embedded graph
Computational Geometry: Theory and Applications
Space complexity of perfect matching in bounded genus bipartite graphs
Journal of Computer and System Sciences
Finding Cycles with Topological Properties in Embedded Graphs
SIAM Journal on Discrete Mathematics
Counting and sampling minimum cuts in genus g graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
Dynamic programming for graphs on surfaces
ACM Transactions on Algorithms (TALG)
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We present an algorithm for finding shortest surface non-separating cycles in graphs embedded on surfaces in $O(g^{3/2}V^{3/2}\log V+g^{5/2}V^{1/2})$ time, where V is the number of vertices in the graph and g is the genus of the surface. If $g=o(V^{1/3})$, this represents an improvement over previous results by Thomassen, and Erickson and Har-Peled. We also give algorithms to find a shortest non-contractible cycle in $O(g^{O(g)}V^{3/2})$ time, which improves previous results for fixed genus. This result can be applied for computing the face-width and the non-separating face-width of embedded graphs. Using similar ideas we provide the first near-linear running time algorithm for computing the face-width of a graph embedded on the projective plane, and an algorithm to find the face-width of embedded toroidal graphs in $O(V^{5/4}\log V)$ time.