Optimizing Logic Programs with Finite Domain Constraints

Combinatorial problems are often speciied declaratively in logic programs with constraints over nite domains. This paper presents several program transformation and optimization techniques for improving the performance of the class of programs with nite-domain constraints. The techniques include planning the evaluation order of body goals, reducing the domain of variables, planning the instantiation order of variable values, and controlling process granularity and scheduling processes among processors in parallel or distributed systems. The techniques are based on the information about the number of solutions of combinatorial problems. Since the decision versions of many combinatorial problems are NP-complete, if P 6 = NP, there is no polynomial time algorithm for computing the number of solutions for combinatorial problems. This paper presents a simple greedy approximation algorithm for estimating the number of solutions for combinatorial problems over nite domains. Based on this simple algorithm, a class of exible polynomial time algorithms is also developed.