SIAM Journal on Computing
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Computing sums of radicals in polynomial time
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SIAM Journal on Computing
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Topology for Computing
Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Finding shortest contractible and shortest separating cycles in embedded graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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 contractible and shortest separating cycles in embedded graphs
ACM Transactions on Algorithms (TALG)
Optimal homologous cycles, total unimodularity, and linear programming
Proceedings of the forty-second ACM symposium on Theory of computing
Finding shortest non-trivial cycles in directed graphs on surfaces
Proceedings of the twenty-sixth annual symposium on Computational geometry
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
Optimal Homologous Cycles, Total Unimodularity, and Linear Programming
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
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
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Let M be an orientable combinatorial surface. A cycle on M is splitting if it has no self-intersections and it partitions M into two components, neither of which is homeomorphic to a disk. In other words, splitting cycles are simple, separating, and non-contractible. We prove that finding the shortest splitting cycle on a combinatorial surface is NP-hard but fixed-parameter tractable with respect to the surface genus g and the number of boundary components b of the surface. Specifically, we describe an algorithm to compute the shortest splitting cycle in (g+b)^O^(^g^+^b^)nlogn time, where n is the complexity of the combinatorial surface.