On the Maximum Weight Minimal Separator

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)


Given an undirected and connected graph \(G=(V, E)\) and two vertices \(s, t\in V\), a vertex subset S that separates s and t is called an s-t separator, and an s-t separator is called minimal if no proper subset of S separates s and t. In this paper, we consider finding a minimal s-t separator with maximum weight on a vertex-weighted graph. We first prove that this problem is NP-hard. Then, we propose an \(\mathbf{tw}^{O(\mathbf{tw})}n\)-time deterministic algorithm based on tree decompositions. Moreover, we also propose an \(O^*(9^\mathbf{tw}\cdot W^2)\)-time randomized algorithm to determine whether there exists a minimal s-t separator where W is its weight and \(\mathbf{tw}\) is the treewidth of G.


Parameterized algorithm Minimal separator Treewidth 



We are grateful to Dr. Jesper Nederlof for helpful discussions.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Economic EngineeringKyushu UniversityFukuokaJapan
  2. 2.Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands
  3. 3.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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