Global Minimum Cuts in Surface-Embedded Graphs
Years and Authors of Summarized Original Work
2009; Chambers, Erickson, Nayyeri
2011; Erickson, Nayyeri
2012; Erickson, Fox, Nayyeri
Given a graph G in which every edge has a nonnegative capacity, the goal of the minimum-cut problem is to find a subset of edges of G with minimum total capacity whose deletion disconnects G. The closely related minimum (s, t)-cut problem further requires two specific vertices s and t to be separated by the deleted edges. Minimum cuts and their generalizations play a central role in divide-and-conquer and network optimization algorithms.
The fastest algorithms known for computing minimum cuts in arbitrary graphs run in roughly O(mn) time for graphs with n vertices and medges. However, even faster algorithms are known for graphs with additional topological structure. This entry sketches algorithms to compute minimum cuts in near-linear time when the input graph can be drawn on a surface with bounded genus – informally, a sphere with a...
KeywordsTopological graph theory Graph embedding Minimum cuts Homology Covering spaces Fixed-parameter tractability
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