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The Complexity of Acyclic Subhypergraph Problems

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WALCOM: Algorithms and Computation (WALCOM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6552))

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Abstract

We investigate the computational complexity of two decision problems concerning the existence of certain acyclic subhypergraphs of a given hypergraph, namely the Spanning Acyclic Subhypergraph problem and the Maximum Acyclic Subhypergraph problem. The former is about the existence of an acyclic subhypergraph such that each vertex of the input hypergraph is contained in at least one hyperedge of the subhypergraph. The latter is about the existence of an acyclic subhypergraph with k hyperedges where k is part of the input. For each of these problems, we consider different notions of acyclicity of hypergraphs: Berge-acyclicity, γ-acyclicity, β-acyclicity and α-acyclicity. We are also concerned with the size of the hyperedges of the input hypergraph. Depending on these two parameters (notion of acyclicity and size of the hyperedges), we try to determine which instances of the two problems are in P ∩ RNC and which are NP-complete.

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Authors and Affiliations

  1. Équipe de Logique Mathématique (FRE 3233) - Université Paris Diderot, Paris, 7, France

    David Duris & Yann Strozecki

Authors
  1. David Duris
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  2. Yann Strozecki
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Editors and Affiliations

  1. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  2. Department of Computer Science and Engineering, Hauz Khas, Indian Institute of Technology, 11016, New Delhi, India

    Amit Kumar

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Duris, D., Strozecki, Y. (2011). The Complexity of Acyclic Subhypergraph Problems. In: Katoh, N., Kumar, A. (eds) WALCOM: Algorithms and Computation. WALCOM 2011. Lecture Notes in Computer Science, vol 6552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19094-0_7

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  • DOI: https://doi.org/10.1007/978-3-642-19094-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19093-3

  • Online ISBN: 978-3-642-19094-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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