Guiding SAT Solving by Formula Partitioning

Abstract

When deciding the satisfiability of a Boolean formula, one promising approach is to split the formula into two smaller independent sub-formulas. While many studies report encouraging early results with such methods, the approach is rarely used in state-of-the-art solvers. In this paper, we present a technique that uses formula partitioning to guide the solution of the SAT problem through providing initialization values for the VSIDS heuristic. Our results on a large number of benchmark instances show that the method can notably improve the performance of modern solvers, especially if the time available for solving is short. We also present some findings in the area of hypergraph partitioning, which is used as a tool for our technique.

More Recent Advances in (Hyper)Graph Partitioning

“…One representation is the dual representation with clauses as vertices and variables as hyperedges, consisting of clauses that contain the variable (either negated or not). Mann and Papp [136] use balanced bipartitioning to identify variables that branching solvers should focus on assigning first, such that the formula is split into two once variables in the cut are assigned. The two sub-formulas can be solved independently, which is expected to be faster.…”