On the maximum weight minimal separator

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

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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 - Dec 3 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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