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An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs

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Combinatorial Algorithms (IWOCA 2019)

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Abstract

A chordal bipartite graph is a bipartite graph without induced cycles with length six or more. As the main result of our paper, we propose an enumeration algorithm  which enumerates all chordal bipartite induced subgraphs in \(O(kt\varDelta ^2)\) time per solution on average, where k is the degeneracy of G, t is the maximum size of \(K_{t,t}\) as an induced subgraph of G, and \(\varDelta \) is the maximum degree of G. To achieve the above time complexity, we introduce a new characterization of chordal bipartite graphs, called CBEO. This characterization is based on the relation between a \(\beta \)-acyclic hypergraph and its incidence graph. As a corollary,  achieves constant amortized time enumeration for bounded degree graphs.

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Authors and Affiliations

  1. IST, Hokkaido University, Sapporo, Japan

    Kazuhiro Kurita & Hiroki Arimura

  2. National Institute of Informatics, Tokyo, Japan

    Kunihiro Wasa & Takeaki Uno

Authors
  1. Kazuhiro Kurita
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  2. Kunihiro Wasa
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  3. Takeaki Uno
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  4. Hiroki Arimura
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Corresponding author

Correspondence to Kazuhiro Kurita .

Editor information

Editors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Charles J. Colbourn

  2. University of Pisa, Pisa, Italy

    Roberto Grossi

  3. University of Pisa, Pisa, Italy

    Nadia Pisanti

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Kurita, K., Wasa, K., Uno, T., Arimura, H. (2019). An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs. In: Colbourn, C., Grossi, R., Pisanti, N. (eds) Combinatorial Algorithms. IWOCA 2019. Lecture Notes in Computer Science(), vol 11638. Springer, Cham. https://doi.org/10.1007/978-3-030-25005-8_28

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  • DOI: https://doi.org/10.1007/978-3-030-25005-8_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25004-1

  • Online ISBN: 978-3-030-25005-8

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