Multicut is FPT

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Abstract

Let G=(V,E) be a graph on n vertices and R be a set of pairs of vertices in V called requests. A multicut is a subset F of E such that every request xy of R is cut by F, i.e. every xy-path of G intersects F. We show that there exists an O(f(k)nc) algorithm which decides if there exists a multicut of size at most k. In other words, the Multicut problem parameterized by the solution size k is Fixed-Parameter Tractable. © 2011 ACM.

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Bousquet, N., Daligault, J., & Thomassé, S. (2011). Multicut is FPT. In Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 459–468). Association for Computing Machinery. https://doi.org/10.1145/1993636.1993698

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