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Minimum Cuts and Shortest Homologous Cycles (2009)
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| Venue: | SYMPOSIUM ON COMPUTATIONAL GEOMETRY |
| Citations: | 33 - 11 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.
Keyphrases
minimum cut shortest homologous cycle minimum-cost subgraph single input cycle surface-embedded graph nearlinear time specified vertex minimum-cut algorithm orientable surface undirected graph z2-homology class slight generalization general sparse graph first algorithm time algorithm embedded graph planar graph special case previous time bound
