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A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments

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Algorithms and Computation (ISAAC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7074))

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Abstract

In the k -Feedback Arc/Vertex Set problem we are given a directed graph D and a positive integer k and the objective is to check whether it is possible to delete at most k arcs/vertices from D to make it acyclic. Dom et al.[CIAC, 2006] initiated a study of the Feedback Arc Set problem on bipartite tournaments (k -FASBT) in the realm of parameterized complexity. They showed that k -FASBT can be solved in time O(3.373k n 6) on bipartite tournaments having n vertices. However, until now there was no known polynomial sized problem kernel for k -FASBT. In this paper we obtain a cubic vertex kernel for k -FASBT. This completes the kernelization picture for the Feedback Arc/Vertex Set problem on tournaments and bipartite tournaments, as for all other problems polynomial kernels were known before. We obtain our kernel using a non-trivial application of “independent modules” which could be of independent interest.

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Authors and Affiliations

  1. Chennai Mathematical Institute, Chennai, India

    Pranabendu Misra

  2. The Institute of Mathematical Sciences, Chennai, India

    Venkatesh Raman, M. S. Ramanujan & Saket Saurabh

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  1. Pranabendu Misra
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  2. Venkatesh Raman
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  3. M. S. Ramanujan
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  4. Saket Saurabh
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Editor information

Editors and Affiliations

  1. Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan

    Takao Asano

  2. Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

  3. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Yoshio Okamoto

  4. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552, Tokyo, Japan

    Osamu Watanabe

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Misra, P., Raman, V., Ramanujan, M.S., Saurabh, S. (2011). A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_35

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  • DOI: https://doi.org/10.1007/978-3-642-25591-5_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25590-8

  • Online ISBN: 978-3-642-25591-5

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