Revisiting Graph Width Measures for CNF-Encodings
| Autor: | Stefan Mengel, Romain Wallon |
|---|---|
| Přispěvatelé: | Centre de Recherche en Informatique de Lens (CRIL), Université d'Artois (UA)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
050101 languages & linguistics Logarithm Computer science 05 social sciences 02 engineering and technology Graph [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] Auxiliary variables Treewidth Combinatorics Bounding overwatch Artificial Intelligence Bounded function 0202 electrical engineering electronic engineering information engineering Graph (abstract data type) 020201 artificial intelligence & image processing 0501 psychology and cognitive sciences Computational problem Communication complexity Mathematics |
| Zdroj: | Theory and Applications of Satisfiability Testing-SAT 2019 22nd International Conference on Theory and Applications of Satisfiability Testing (SAT'19) 22nd International Conference on Theory and Applications of Satisfiability Testing (SAT'19), Jul 2019, Lisbon, Portugal. pp.222-238, ⟨10.1007/978-3-030-24258-9_16⟩ Lecture Notes in Computer Science ISBN: 9783030242572 SAT |
| ISSN: | 1076-9757 |
| DOI: | 10.1613/jair.1.11750 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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