## Faster shortest non-contractible cycles in directed surface graphs

Venue: | CoRR |

Citations: | 1 - 0 self |

### BibTeX

@ARTICLE{Fox_fastershortest,

author = {Kyle Fox},

title = {Faster shortest non-contractible cycles in directed surface graphs},

journal = {CoRR},

year = {},

pages = {2011}

}

### OpenURL

### Abstract

Let G be a directed graph embedded on a surface of genus g with b boundary cycles. We describe an algorithm to compute the shortest non-contractible cycle in G in O((g 3 + g b)n log n) time. Our algorithm improves the previous best known time bound of (g + b) O(g+b) n log n for all positive g and b. We also describe an algorithm to compute the shortest non-null-homologous cycle in G in O((g 2 + g b)n log n) time, generalizing a known algorithm to compute the shortest non-separating cycle.

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Citation Context ...thm for computing the shortest non-separating cycle that relies on computing the shortest cycle in each of 2O(g) homology classes. The latest results for these problems are two algorithms of Erickson =-=[19]-=-. The first algorithm computes shortest non-separating cycles in O(g 2n log n) time by computing shortest paths in several linear sized covering spaces. The second algorithm computes shortest non-cont... |

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