Multicut in trees viewed through the eyes of vertex cover

Authors:
Jianer Chen;Jia-Hao Fan;Iyad A. Kanj;Yang Liu;Fenghui Zhang
Affiliations:
Department of Computer Science and Engineering, Texas A&M University, College Station, TX;Department of Computer Science and Engineering, Texas A&M University, College Station, TX;School of Computing, DePaul University, Chicago, IL;Department of Computer Science, University of Texas-Pan American, Edinburg, TX;Google Kirkland, Kirkland, WA
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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Abstract

We take a new look at the multicut problem in trees through the eyes of the VERTEX cover problem. This connection, together with other techniques that we develop, allows us to significantly improve the O(k6) upper bound on the kernel size for multicut, given by Bousquet et al., to O(k3). We exploit this connection further to present a parameterized algorithm for multicut that runs in time O*(ρk), where ρ = (√5+1)/2 ≈ 1.618. This improves the previous (time) upper bound of O*(2k), given by Guo and Niedermeier, for the problem.