Community Structure in Industrial SAT Instances

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental process. It is believed that these techniques exploit the underlying structure of industrial instances. However, there are few works trying to exactly characterize the main features of this structure. The research community on complex networks has developed techniques of analysis and algorithms to study real-world graphs that can be used by the SAT community. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them. In this paper, inspired by the results on complex networks, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. In our analysis, we represent SAT instances as graphs, and we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erd\"os-R\'enyi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver. In particular, we use the community structure to detect that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. This is, learned clauses tend to contain variables of distinct communities

Community structure in industrial SAT instances

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. It is believed that most of these successful techniques exploit the underlying structure of industrial instances. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them. In this paper, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. Representing SAT instances as graphs, we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erdös-Rényi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver, and observe that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. Motivated by this observation, we finally present an application that exploits the community structure to detect relevant learned clauses, and we show that detecting these clauses results in an improvement on the performance of the SAT solver. Empirically, we observe that this improves the performance of several SAT solvers on industrial SAT formulas, especially on satisfiable instances.Peer ReviewedPostprint (published version

Semaine d'Etude Mathématiques et Entreprises 1 : Modèles de comparaison quantitative de matrices 3D

Air Liquide dispose de jeux de données représentant des champs de quantité de dépôt de particules sur les poumons. Ces données proviennent de mesures 3D (obtenues via SPECT, Single Photon Emission Computer Tomography) du dépôt d'un aérosol contenant des particules radio-labellisées préalablement inhalé par les patients étudiés. Le sujet proposé ici consiste à se demander quelles sont les méthodes permettant de comparer de façon quantitative et systématique les résultats des observations, qui sont donnés sous la forme de matrices 3D correspondant à la quantité de particules estimée dans chaque voxel

Absence of dystrophin in mice reduces NO-dependent vascular function and vascular density: total recovery after a treatment with the aminoglycoside gentamicin.

International audienceOBJECTIVE: Mutations in the dystrophin gene causing Duchenne's muscular dystrophy (DMD) lead to premature stop codons. In mice lacking dystrophin (mdx mice), a model for DMD, these mutations can be suppressed by aminoglycosides such as gentamicin. Dystrophin plays a role in flow (shear stress)-mediated endothelium-dependent dilation (FMD) in arteries. We investigated the effect of gentamicin on vascular contractile and dilatory functions, vascular structure, and density in mdx mice. METHODS AND RESULTS: Isolated mice carotid and mesenteric resistance arteries were mounted in arteriographs allowing continuous diameter measurements. Mdx mice showed lower nitric oxide (NO)-dependent FMD and endothelial NO synthase (eNOS) expression as well as decreased vascular density in gracilis and cardiac muscles compared with control mice. Treatment with gentamycin restored these parameters. In contrast, smooth muscle-dependent contractions as well as endothelium-dependent or -independent dilation were not affected by dystrophin deficiency or by gentamicin treatment. CONCLUSIONS: Dystrophin deficiency induces a selective defect in flow-dependent mechanotransduction, thus attenuating FMD and eNOS expression, and may contribute to low arteriolar density. These findings open important perspectives regarding the mechanism involved in the pathophysiology of genetic diseases related to premature stop codons such as DMD