An Analysis of the Impact of Community Structure on SAT Solver Performance
Fischmeister, Sebastian and Ganesh, Vijay
Despite enormous improvements in Boolean SATisfiability solver performance over the last decade, it is still unclear why specific input formula are slow to solve, when other similarly specified formula execute more quickly. This work explores the relationship between the community structure of a SAT formula and its execution time on several state-of-the-art solvers. We explore the analysis of this data from a number of directions; first, we explore the relationship between the well known clause-variable ratio result, and community structure in randomly generated instances. Second, we perform a standard linear regression on data obtained from the 2013 SAT competition. Third, we present a visualisation tool and data repository for viewing the structure of SAT formula. Fourth, we explore the affect of hardware constraints on the solution time of instances across various machines. Finally, we explore survival analysis a technique that is new to the field of Boolean SATisfiability. By collating the results from each of these experiments, we have determined that the community structure is critical in determining the solution time of a SAT formula, more important than the clause-variable ratio of the formula. While this work is far from a last word regarding the solution time of SAT formula, it does go a long way to explain why different similarly specified formula have such different solution times.