BaW 1.0 - A Problem Specific SAT Solver for Effective Strong Connectivity Testing in Sparse Directed Graphs

Abstract

In our previous works, we proved that if a directed graph is strongly connected, then the generated 2-SAT problem is a black-and-white 2-SAT problem, which has two solutions: where each variable is true (the white assignment), and where each variable is false (the black one). We proved also theoretically that these problems could be solved in linear time. In this article we present a DPLL-based problem specific SAT solver called BaW 1.0. Problem specific, because the BaW 1.0 is not a complete SAT solver, it is only validated for our special black-and-white 2-SAT problem based benchmarks. First, we show how to solve the black-and-white 2-SAT problems in linear time and how to use this solver for effective strong connectivity testing in large and sparse directed graphs. After that we present our results on these benchmarks which show that remarkable improvements have taken place in the number of solved instances as well as in the computation time compared to existing modern State-of-the-art SAT solvers (CSFLOC 8, Glucose 3.0).