Sergio Cabello
Jeff Erickson
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, noncontractible, essentially 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 noncontractible or nonseparating 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, a tight octagonal decomposition in O(gnlog n) time, and a shortest contractible cycle enclosing a nonempty set of faces in O(nlog2 n) time.
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Index Terms
- Finding one tight cycle
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