Cao, Yixin and Chen, J and Fan, J (2014) An O* (1.84k) parameterized algorithm for the multiterminal cut problem. INFORMATION PROCESSING LETTERS, 114 (4). pp. 167-173. ISSN 0020-0190 MTMT:2506564; doi:10.1016/j.ipl.2013.12.001

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Abstract

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: maximum volume minimum(s, t) -cuts by Ford and Fulkerson [11] and isolating cuts by Dahlhaus et al. [9]. 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 {dot operator} nO (1) time, thereby breaking the 2k {dot operator} nO (1) barrier. As a by-product, it gives a 1.36k {dot operator} nO (1) time 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 Elsevier B.V.

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