## Minimum Cuts and Shortest Homologous Cycles (2009)

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Venue: | SYMPOSIUM ON COMPUTATIONAL GEOMETRY |

Citations: | 17 - 7 self |

### BibTeX

@INPROCEEDINGS{Chambers09minimumcuts,

author = {Erin Chambers and Jeff Erickson and Amir Nayyeri},

title = {Minimum Cuts and Shortest Homologous Cycles},

booktitle = {SYMPOSIUM ON COMPUTATIONAL GEOMETRY},

year = {2009},

publisher = {}

}

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### Abstract

We describe the first algorithms to compute minimum cuts in surface-embedded graphs in nearlinear time. Given an undirected graph embedded on an orientable surface of genus g, with two specified vertices s and t, our algorithm computes a minimum (s, t)-cut in g O(g) n log n time. Except for the special case of planar graphs, for which O(n log n)-time algorithms have been known for more than 20 years, the best previous time bounds for finding minimum cuts in embedded graphs follow from algorithms for general sparse graphs. A slight generalization of our minimum-cut algorithm computes a minimum-cost subgraph in every Z2-homology class. We also prove that finding a minimum-cost subgraph homologous to a single input cycle is NP-hard.