Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth 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
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Splitting (complicated) surfaces is hard
Proceedings of the twenty-second annual symposium on Computational geometry
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
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
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
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A cycle on a combinatorial surface is tight if it as short as possible in its (free) homotopy class. We describe an algorithm to compute a single tight, non-contractible, simple cycle on a given orientable combinatorial surface in O(n log n) time. The only method previously known for this problem was to compute the globally shortest non-contractible or non-separating cycle in O(min{g3, n} n log n) time, where g is the genus of the surface. As a consequence, we can compute the shortest cycle freely homotopic to a chosen boundary cycle in O(n log n) time and a tight octagonal decomposition in O(gn log n) time.