On the maximum weight minimal separator

Tesshu Hanaka*, Hans L. Bodlaender, Tom C. van der Zanden, Hirotaka Ono

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Web of Science)
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Given an undirected and connected graph G=(V,E) and two vertices s,t∈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. Moreover, we say that a set S is a minimal separator of G if S is a minimal s-t separator for some 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 these problems are NP-hard. On the other hand, we give an O⁎(twO(tw))-time deterministic algorithm based on tree decompositions where O⁎ is the order notation omitting the polynomial factor of n. Moreover, we improve the algorithm by using the Rank-Based approach and the running time is O⁎(38⋅2ω)tw. Finally, we give an O⁎(9tw⋅W2)-time randomized algorithm to determine whether there exists a minimal (s-t) separator where W is its weight and tw is the treewidth of G.
Original languageEnglish
Pages (from-to)294-308
Number of pages15
JournalTheoretical Computer Science
Publication statusPublished - 3 Dec 2019


  • Parameterized algorithm
  • Minimal separator
  • Treewidth

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