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Packing Arc-Disjoint Cycles in Bipartite Tournaments

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WALCOM: Algorithms and Computation (WALCOM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12049))

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Abstract

An r-partite tournament is a directed graph obtained by assigning a unique orientation to each edge of a complete undirected r-partite simple graph. Given a bipartite tournament T on n vertices, we explore the parameterized complexity of the problem of determining if T has a cycle packing (a set of pairwise arc-disjoint cycles) of size k. Although the maximization version of this problem can be seen as the linear programming dual of the well-studied problem of finding a minimum feedback arc set (a set of arcs whose deletion results in an acyclic graph) in bipartite tournaments, surprisingly no algorithmic results seem to exist. We show that this problem can be solved in \(2^{\mathcal {O}(k \log k)} n^{\mathcal {O}(1)}\) time and admits a kernel with \(\mathcal {O}(k^2)\) vertices.

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Author information

Authors and Affiliations

  1. Indian Institute of Technology Madras, Chennai, India

    Ajay Saju Jacob

  2. Indian Institute of Technology Palakkad, Palakkad, India

    R. Krithika

Authors
  1. Ajay Saju Jacob
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  2. R. Krithika
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Correspondence to R. Krithika .

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Editors and Affiliations

  1. Department of CSE, BUET, Dhaka, Bangladesh

    M. Sohel Rahman

  2. Mathematical Informatics, University of Tokyo, Tokyo, Japan

    Kunihiko Sadakane

  3. School of Computing, National University of Singapore, Singapore, Singapore

    Wing-Kin Sung

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Jacob, A.S., Krithika, R. (2020). Packing Arc-Disjoint Cycles in Bipartite Tournaments. In: Rahman, M., Sadakane, K., Sung, WK. (eds) WALCOM: Algorithms and Computation. WALCOM 2020. Lecture Notes in Computer Science(), vol 12049. Springer, Cham. https://doi.org/10.1007/978-3-030-39881-1_21

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  • DOI: https://doi.org/10.1007/978-3-030-39881-1_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-39880-4

  • Online ISBN: 978-3-030-39881-1

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