Multicut in trees viewed through the eyes of vertex cover

Authors:
Jianer Chen;Jia-Hao Fan;Iyad Kanj;Yang Liu;Fenghui Zhang
Affiliations:
Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843, USA;Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843, USA;DePaul University, Chicago, IL 60604, USA;Department of Computer Science, University of Texas-Pan American, Edinburg, TX 78539, USA;Google Kirkland, 747 6th Street South, Kirkland, WA 98033, USA
Venue:
Journal of Computer and System Sciences
Year:
2012

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Abstract

We take a new look at the multicut problem in trees, denoted multicut on trees henceforth, through the eyes of the vertex cover problem. This connection, together with other techniques that we develop, allows us to give an upper bound of O(k^3) on the kernel size for multicut on trees, significantly improving the O(k^6) upper bound given by Bousquet et al. We exploit this connection further to present a parameterized algorithm for multicut on trees that runs in time O^@?(@r^k), where @r=(5+1)/2~1.618. This improves the previous (time) upper bound of O^@?(2^k), given by Guo and Niedermeier, for the problem.