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

by
Kyle Fox

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.