Parameterized complexity dichotomy for Steiner Multicut

Karl Bringmann, Danny Hermelin, Matthias Mnich, Erik Jan Van Leeuwen

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We consider the Steiner Multicut problem, which asks, given an undirected graph G, a collection T={T1,...,Tt}, Ti V(G), of terminal sets of size at most p, and an integer k, whether there is a set S of at most k edges or nodes such that of each set Ti at least one pair of terminals is in different connected components of G-S. We provide a dichotomy of the parameterized complexity of Steiner Multicut. For any combination of k, t, p, and the treewidth tw(G) as constant, parameter, or unbounded, and for all versions of the problem (edge deletion and node deletion with and without deletable terminals), we prove either that the problem is fixed-parameter tractable, W[1]-hard, or (para-)NP-complete. Our characterization includes a dichotomy for Steiner Multicut on trees as well as a polynomial time versus NP-hardness dichotomy (by restricting k,t,p,tw(G) to constant or unbounded).

Original languageEnglish
Pages (from-to)1020-1043
Number of pages24
JournalJournal of Computer and System Sciences
Issue number6
StatePublished - 1 Sep 2016


  • Cut problems
  • Kernelization
  • Parameterized complexity
  • Steiner multicut

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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