Parameterized complexity dichotomy for Steiner multicut

Karl Bringmann, Danny Hermelin, Matthias Mnich, Erik Jan van Leeuwen*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We consider the STEINER MULTICUT problem, which asks, given an undirected graph G, a collection tau = {T-1,, T-t}, T-i subset of 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 T-i 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
Publication statusPublished - Sept 2016


  • Cut problems
  • Steiner multicut
  • Parameterized complexity
  • Kernelization
  • FLOW

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