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Linear-Time Generation of Random Chordal Graphs

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Book cover Algorithms and Complexity (CIAC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10236))

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Abstract

Chordal graphs form one of the most well studied graph classes. Several graph problems that are NP-hard in general become solvable in polynomial time on chordal graphs, whereas many others remain NP-hard. For a large group of problems among the latter, approximation algorithms, parameterized algorithms, and algorithms with moderately exponential or sub-exponential running time have been designed. Chordal graphs have also gained increasing interest during the recent years in the area of enumeration algorithms. Being able to test these algorithms on instances of chordal graphs is crucial for understanding the concepts of tractability of hard problems on graph classes. Unfortunately, only few published papers give algorithms for generating chordal graphs. Even in these papers, only very few methods aim for generating a large variety of chordal graphs. Surprisingly, none of these methods is based on the “intersection of subtrees of a tree” characterization of chordal graphs. In this paper, we give an algorithm for generating chordal graphs, based on the characterization that a graph is chordal if and only if it is the intersection graph of subtrees of a tree. The complexity of our algorithm is linear in the size of the produced graph. We give test results to show the variety of chordal graphs that are produced, and we compare these results to existing results.

This work is supported by the Research Council of Norway, Bogazici University Research Fund (grant 11765), and Turkish Academy of Sciences GEBIP award.

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Authors and Affiliations

  1. Department of Industrial Engineering, Boğaziçi University, Istanbul, Turkey

    Oylum Şeker, Tınaz Ekim & Z. Caner Taşkın

  2. Department of Informatics, University of Bergen, Bergen, Norway

    Pinar Heggernes

Authors
  1. Oylum Şeker
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  2. Pinar Heggernes
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  3. Tınaz Ekim
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  4. Z. Caner Taşkın
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Correspondence to Oylum Şeker .

Editor information

Editors and Affiliations

  1. National Technical University of Athens, Zografou, Athens, Greece

    Dimitris Fotakis

  2. National Technical University of Athens, Zografou, Athens, Greece

    Aris Pagourtzis

  3. Université Paris-Dauphine, Paris, France

    Vangelis Th. Paschos

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Şeker, O., Heggernes, P., Ekim, T., Taşkın, Z.C. (2017). Linear-Time Generation of Random Chordal Graphs. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_37

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  • DOI: https://doi.org/10.1007/978-3-319-57586-5_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57585-8

  • Online ISBN: 978-3-319-57586-5

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