Finding one tight cycle

Submitted to the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (2008).

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Abstract:

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.

Publications - Jeff Erickson (jeffe@cs.uiuc.edu) 11 Jul 2007