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Multicut in Trees Viewed through the Eyes of Vertex Cover

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Algorithms and Data Structures (WADS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6844))

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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(k 6) upper bound on the kernel size for multicut, given by Bousquet et al., to O(k 3). We exploit this connection further to present a parameterized algorithm for multicut that runs in time O *(ρ k), where \(\rho = (\sqrt{5} + 1)/2 \approx 1.618\). This improves the previous (time) upper bound of O *(2k), given by Guo and Niedermeier, for the problem.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, 77843, USA

    Jianer Chen & Jia-Hao Fan

  2. School of Computing, DePaul University, 243 S. Wabash Avenue, Chicago, IL, 60604, USA

    Iyad A. Kanj

  3. Department of Computer Science, University of Texas-Pan American, Edinburg, TX, 78539, USA

    Yang Liu

  4. Google Kirkland, 747 6th Street South, Kirkland, WA, 98033, United States

    Fenghui Zhang

Authors
  1. Jianer Chen
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  2. Jia-Hao Fan
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  3. Iyad A. Kanj
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  4. Yang Liu
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  5. Fenghui Zhang
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science and Engineering, Polytechnic Institute of New York University, 5 MetroTech Center, 11201, New York, NY, USA

    John Iacono

  3. School of Computer Science, Herzberg Laboratories, Carleton University, Herzberg Building, Room 5350, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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© 2011 Springer-Verlag Berlin Heidelberg

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Chen, J., Fan, JH., Kanj, I.A., Liu, Y., Zhang, F. (2011). Multicut in Trees Viewed through the Eyes of Vertex Cover. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_19

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  • DOI: https://doi.org/10.1007/978-3-642-22300-6_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22299-3

  • Online ISBN: 978-3-642-22300-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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