## Shortest non-trivial cycles in directed surface graphs (2011)

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by
Jeff Erickson

Venue: | In Proc. 27th Ann. Symp. Comput. Geom |

Citations: | 4 - 2 self |

### BibTeX

@INPROCEEDINGS{Erickson11shortestnon-trivial,

author = {Jeff Erickson},

title = {Shortest non-trivial cycles in directed surface graphs},

booktitle = {In Proc. 27th Ann. Symp. Comput. Geom},

year = {2011},

pages = {236--243}

}

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### Abstract

Let G be a directed graph embedded on a surface of genus g. We describe an algorithm to compute the shortest non-separating cycle in G in O(g 2 n log n) time, exactly matching the fastest algorithm known for undirected graphs. We also describe an algorithm to compute the shortest non-contractible cycle in G in g O(g) n log n time, matching the fastest algorithm for undirected graphs of constant genus.