## 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(gn log n) time, and a shortest contractible cycle enclosing a nonempty set of faces in O(n log2 n) time.

Original language | English (US) |
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Article number | 61 |

Journal | ACM Transactions on Algorithms |

Volume | 6 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2010 |

## Keywords

- Combinatorial surface
- Noncontractible cycle
- Nonseparating cycle
- Topological graph theory

## ASJC Scopus subject areas

- Mathematics (miscellaneous)