On solving Boolean combinations of generalized 2SAT constraints

Abstract: "We consider the satisfiability problem for Boolean combinations of generalized 2SAT constraints, which are linear constraints with at most two, possibly unbounded, integer variables having coefficients in [-1, 1]. We prove that if a satisfying solution exists, then there is a solution with each variable taking values in [-n ┬╖ ([superscript b]max + 1), n ┬╖ ([superscript b]max + 1)], where n is the number of variables, and b[subscript max] is the maximum over the absolute values of constants appearing in the constraints. This solution bound improves over previously obtained bounds by an exponential factor. Our result enables a new enumerative approach to satisfiability checking. An experimental evaluation demonstrates the efficiency of this approach over previous techniques. As a corollary of our main result, we obtain a polynomial-time algorithm for approximating optima of generalized 2SAT integer programs to within an additive factor."