Algorithms and complexity results for #SAT and Bayesian inference

Bacchus, Fahiem; Dalmao, Shannon; Pitassi, Toniann

doi:10.1109/sfcs.2003.1238208

Cited by 86 publications

(121 citation statements)

References 17 publications

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107

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“…It is well known that #SAT on formulas of bounded primal treewidth is linear-time tractable [23]. A similar result has been shown in terms of the branchwidth of formulas [1], a parameter that is equivalent to primal treewidth. The incidence treewidth of a formula is the treewidth of its incidence graph.…”

Section: Related Structural Parameterssupporting

confidence: 61%

“…For a formula F , we let F X = { C X | C ∈ F } \ {∅}. For a truth assignment τ , we let clause(τ ) = τ −1 (0) ∪ τ −1 (1). This leads to the following lemma.…”

Section: Preliminariesmentioning

confidence: 99%

“…Recall that |S t | ≤ (|F | + 1) k for all nodes t ∈ V T due to (1). This bound on the number of transferable equivalence classes for a node t has the following two consequences.…”

Section: Theoremmentioning

confidence: 99%

“…The aim of this paper is to harness its power for propositional model counting (#SAT), a well-studied problem with various applications in artifical intelligence, such as probabilistic inference [1]. We consider CNF formulas whose incidence graph incidence β-hypertree width incidence clique-width modular incidence treewidth signed incidence clique-width incidence treewidth primal treewidth Figure 1 Hierarchy of structural parameters.…”

Section: Introductionmentioning

confidence: 99%

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Model Counting for CNF Formulas of Bounded Modular Treewidth

2015

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The modular treewidth of a graph is its treewidth after the contraction of modules. Modular treewidth properly generalizes treewidth and is itself properly generalized by clique-width. We show that the number of satisfying assignments of a CNF formula whose incidence graph has bounded modular treewidth can be computed in polynomial time. This provides new tractable classes of formulas for which #SAT is polynomial. In particular, our result generalizes known results for the treewidth of incidence graphs and is incomparable with known results for cliquewidth (or rank-width) of signed incidence graphs. The contraction of modules is an effective data reduction procedure. Our algorithm is the first one to harness this technique for #SAT. The order of the polynomial time bound of our algorithm depends on the modular treewidth. We show that this dependency cannot be avoided subject to an assumption from Parameterized Complexity. ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems

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Section: Related Structural Parameterssupporting

confidence: 61%

“…For a formula F , we let F X = { C X | C ∈ F } \ {∅}. For a truth assignment τ , we let clause(τ ) = τ −1 (0) ∪ τ −1 (1). This leads to the following lemma.…”

Section: Preliminariesmentioning

confidence: 99%

“…Recall that |S t | ≤ (|F | + 1) k for all nodes t ∈ V T due to (1). This bound on the number of transferable equivalence classes for a node t has the following two consequences.…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Model Counting for CNF Formulas of Bounded Modular Treewidth

2015

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“…Besides its well-known theoretical relevancy, the problem of counting models of Boolean Satisfiability (SAT) formulas (#SAT) has a large number of key application areas [2,18]. Recent years have seen significant improvements in algorithms for #SAT, which include the utilization of well-known SAT techniques as well as the identification of connected components and component caching, but also variable lifting and blocking clauses [6,12,17,18].…”

Section: Introductionmentioning

confidence: 99%

Counting Models in Integer Domains

Morgado

Matos

Manquinho

et al. 2006

Lecture Notes in Computer Science

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Abstract. This paper addresses the problem of counting models in integer linear programming (ILP) using Boolean Satisfiability (SAT) techniques, and proposes two approaches to solve this problem. The first approach consists of encoding ILP instances into pseudo-Boolean (PB) instances. Moreover, the paper introduces a model counter for PB constraints, which can be used for counting models in PB as well as in ILP. A second alternative approach consists of encoding instances of ILP into instances of SAT. A two-step procedure is proposed, consisting of first mapping the ILP instance into PB constraints and then encoding the PB constraints into SAT. One key observation is that not all existing PB to SAT encodings can be used for counting models. The paper provides conditions for PB to SAT encodings that can be safely used for model counting, and proves that some of the existing encodings are safe for model counting while others are not. Finally, the paper provides experimental results, comparing the PB and SAT approaches, as well as existing alternative solutions.

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Tangle bases: Revisited

Hicks

Brimkov

2020

Networks

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The concept of branch decomposition was first introduced by Robertson and Seymour in their proof of the Graph Minors Theorem, and can be seen as a measure of the global connectivity of a graph. Since then, branch decomposition and branchwidth have been used for computationally solving combinatorial optimization problems modeled on graphs and matroids. General branchwidth is the extension of branchwidth to any symmetric submodular function defined over a finite set. General branchwidth encompasses graphic branchwidth, matroidal branchwidth, and rankwidth. A tangle basis is related to a tangle, a notion also introduced by Robertson and Seymour; however, a tangle basis is more constructive in nature. It was shown in [I. V. Hicks. Graphs, branchwidth, and tangles! Oh my! Networks, 45:55-60, 2005] that a tangle basis of order k is coextensive to a tangle of order k. In this paper, we revisit the construction of tangle bases computationally for other branchwidth parameters and show that the tangle basis approach is still competitive for computing optimal branch decompositions for general branchwidth.

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Algorithms and complexity results for #SAT and Bayesian inference

Abstract: Abstract

Cited by 86 publications

References 17 publications

Model Counting for CNF Formulas of Bounded Modular Treewidth

Model Counting for CNF Formulas of Bounded Modular Treewidth

Counting Models in Integer Domains

Tangle bases: Revisited

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