Global minimum cuts in surface embedded graphs

8 years 5 months ago
Global minimum cuts in surface embedded graphs
We give a deterministic algorithm to find the minimum cut in a surface-embedded graph in near-linear time. Given an undirected graph embedded on an orientable surface of genus g, our algorithm computes the minimum cut in gO(g) nloglog n time, matching the running time of the fastest algorithm known for planar graphs, due to Ł ˛acki and Sankowski, for any constant g. Indeed, our algorithm calls Ł ˛acki and Sankowski’s recent O(nloglog n) time planar algorithm as a subroutine. Previously, the best time bounds known for this problem followed from two algorithms for general sparse graphs: a randomized algorithm of Karger that runs in O(nlog3 n) time and succeeds with high probability, and a deterministic algorithm of Nagamochi and Ibaraki that runs in O(n2 log n) time. We can also achieve a deterministic gO(g) n2 loglog n time bound by repeatedly applying the best known algorithm for minimum (s, t)-cuts in surface graphs. The bulk of our work focuses on the case where the dual of t...
Jeff Erickson, Kyle Fox, Amir Nayyeri
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where SODA
Authors Jeff Erickson, Kyle Fox, Amir Nayyeri
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