An O*(1.84k) parameterized algorithm for the multiterminal cut problem

Yixin Cao, Jianer Chen, Jia Hao Fan

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

2 Citations (Scopus)


We study the multiterminal cut problem, which, given an n-vertex graph whose edges are integer-weighted and a set of terminals, asks for a partition of the vertex set such that each terminal is in a distinct part, and the total weight of crossing edges is at most k. Our weapons shall be two classical results known for decades. One is max volume min (s,t)-cuts by [Ford and Fulkerson, Flows in Networks. Princeton University Press, 1962], and the other is isolating cuts by [Dahlhaus et al., The complexity of multiterminal cuts. SIAM J. Comp. 23(4), 1994]. We sharpen these old weapons with the help of submodular functions, and apply them to this problem, which enable us to design a more elaborated branching scheme on deciding whether a non-terminal vertex is with a terminal or not. This bounded search tree algorithm can be shown to run in 1.84k·nO(1), thereby breaking the 2k·nO(1)barrier. As a by-product, it gives a 1.36k·nO(1)algorithm for 3-terminal cut. The preprocessing applied on non-terminal vertices might be of use for study of this problem from other aspects.
Original languageEnglish
Title of host publicationFundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings
Number of pages11
Publication statusPublished - 3 Sep 2013
Externally publishedYes
Event19th International Symposium on Fundamentals of Computation Theory, FCT 2013 - Liverpool, United Kingdom
Duration: 19 Aug 201321 Aug 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8070 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Symposium on Fundamentals of Computation Theory, FCT 2013
Country/TerritoryUnited Kingdom

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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