An O*(1.84k) Parameterized Algorithm for the Multiterminal Cut Problem Conference Paper uri icon


  • 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 1.84knO(1), thereby breaking the 2 knO(1) barrier. As a by-product, it gives a 1.36knO(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. 2013 Springer-Verlag.

name of conference

  • Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Liverpool, UK, August 19-21, 2013. Proceedings

published proceedings

  • Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

author list (cited authors)

  • Cao, Y., Chen, J., & Fan, J.

citation count

  • 1

complete list of authors

  • Cao, Yixin||Chen, Jianer||Fan, Jia-Hao

publication date

  • September 2013