Despite enormous improvements in Boolean SATisfiability solver performanceover the last decade, it is still unclear why specific input formula are slowto solve, when other similarly specified formula execute more quickly. Thiswork explores the relationship between the community structure of a SATformula and its execution time on several state-of-the-art solvers. We explorethe analysis of this data from a number of directions; first, we explore therelationship between the well known clause-variable ratio result, and com-munity structure in randomly generated instances. Second, we perform astandard linear regression on data obtained from the 2013 SAT competition.Third, we present a visualisation tool and data repository for viewing thestructure of a SAT formula. Fourth, we explore the effect of hardware con-straints on the solution time of instances across various machines. Finally,we explore survival analysis, a technique that is new to the field of BooleanSATisfiability. By collating the results from each of these experiments, wehave determined that the community structure is critical in determining thesolution time of a SAT formula, more important than the clause-variableratio of the formula. While this work is not a complete explanation of thevarying solution time of SAT formulae, it has provided us with significantinsight for further research to answer the question: why different similarlyspecified formula have such different solution times?
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An Analysis of the Effect of Community Structure on SAT Solver Performance