A near-linear time minimum Steiner cut algorithm for planar graphs

12/23/2019

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by   Stephen Jue, et al.

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We consider the Minimum Steiner Cut problem on undirected planar graphs with non-negative edge weights. This problem involves finding the minimum cut of the graph that separates a specified subset X of vertices (terminals) into two parts. This problem is of theoretical interest because it generalizes two classical optimization problems, Minimum s-t Cut and Minimum Cut, and of practical importance because of its application to computing a lower bound for Steiner (Subset) TSP. Our algorithm has running time O(nlognlogk) where k is the number of terminals.