Given an edge-weighted undirected graph and a list of k source-sink pairs of vertices, the well-known minimum multicut problem consists in selecting a minimum-weight set of edges whose removal leaves no path between every source and its corresponding sink. We give the first polynomial-time algorithm to solve this problem in planar graphs, when k is fixed. Previously, this problem was known to remain NP-hard in general graphs with fixed k, and in trees with arbitrary k; the most noticeable tractable case known so far was in planar graphs with fixed k and sources and sinks lying on the outer face. © 2012 Springer-Verlag.
CITATION STYLE
Bentz, C. (2012). A polynomial-time algorithm for planar multicuts with few source-sink pairs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7535 LNCS, pp. 109–119). https://doi.org/10.1007/978-3-642-33293-7_12
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