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We consider the Minimum Steiner Cut problem on undirected planar graphs withnon-negative edge weights. This problem involves finding the minimum cut of thegraph that separates a specified subset $X$ of vertices (terminals) into twoparts. This problem is of theoretical interest because it generalizes twoclassical optimization problems, Minimum $s$-$t$ Cut and Minimum Cut, and ofpractical importance because of its application to computing a lower bound forSteiner (Subset) TSP. Our algorithm has running time $O(n\log{n}\log{k})$ where$k$ is the number of terminals.

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