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Link to original content: https://unpaywall.org/10.1007/978-3-030-24258-9_16
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Revisiting Graph Width Measures for CNF-Encodings

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Theory and Applications of Satisfiability Testing – SAT 2019 (SAT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11628))

Abstract

We consider bounded width CNF-formulas where the width is measured by popular graph width measures on graphs associated to CNF-formulas. Such restricted graph classes, in particular those of bounded treewidth, have been extensively studied for their uses in the design of algorithms for various computational problems on CNF-formulas. Here we consider the expressivity of these formulas in the model of clausal encodings with auxiliary variables. We first show that bounding the width for many of the measures from the literature leads to a dramatic loss of expressivity, restricting the formulas to such of low communication complexity. We then show that the width of optimal encodings with respect to different measures is strongly linked: there are two classes of width measures, one containing primal treewidth and the other incidence cliquewidth, such that in each class the width of optimal encodings only differs by constant factors. Moreover, between the two classes the width differs at most by a factor logarithmic in the number of variables. Both these results are in stark contrast to the setting without auxiliary variables where all width measures we consider here differ by more than constant factors and in many cases even by linear factors.

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Acknowledgements

The authors are grateful to the anonymous reviewers for their comments, which greatly helped to improve the presentation of the paper. The first author would also like to thank David Mitchell for asking the right question at the right moment. This paper grew largely out of an answer to this question.

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Authors and Affiliations

  1. CRIL-CNRS UMR 8188, 62307, Lens, France

    Stefan Mengel & Romain Wallon

  2. Université d’Artois, Lens, France

    Romain Wallon

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  1. Stefan Mengel
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  2. Romain Wallon
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Correspondence to Romain Wallon .

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Editors and Affiliations

  1. University of Lisbon, Lisbon, Portugal

    Mikoláš Janota

  2. University of Lisbon, Lisbon, Portugal

    Inês Lynce

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Mengel, S., Wallon, R. (2019). Revisiting Graph Width Measures for CNF-Encodings. In: Janota, M., Lynce, I. (eds) Theory and Applications of Satisfiability Testing – SAT 2019. SAT 2019. Lecture Notes in Computer Science(), vol 11628. Springer, Cham. https://doi.org/10.1007/978-3-030-24258-9_16

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  • DOI: https://doi.org/10.1007/978-3-030-24258-9_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24257-2

  • Online ISBN: 978-3-030-24258-9

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