Finding shortest non-trivial cycles in directed graphs on surfaces
Proceedings of the twenty-sixth annual symposium on Computational geometry
Technical Section: Tiling surfaces with cylinders using n-loops
Computers and Graphics
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third 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
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An essential cycle on a surface is a simple cycle that cannot be continuously deformed to a point or a single boundary. We describe algorithms to compute the shortest essential cycle in an orientable combinatorial surface in O(n 2log n) time, or in O(nlog n) time when both the genus and number of boundaries are fixed. Our results correct an error in a paper of Erickson and Har-Peled (Discrete Comput. Geom. 31(1):37–59, 2004).