Methods for Parallelizing Constraint Propagation through the Use of Strong Local Consistencies

Abstract

Constraint programming (CP) is a powerful paradigm for various types of hard combinatorial problems. Constraint propagation techniques, such as arc consistency (AC), are used within solvers to prune inconsistent values from the domains of the variables and narrow down the search space. Local consistencies stronger than AC have the potential to prune the search space even more, but they are not widely used because they incur a high run time penalty in cases where they are unsuccessful. All constraint propagation techniques are sequential by nature, and thus they cannot be scaled up to modern multicore machines. For this reason, research on parallelizing constraint propagation is very limited. Contributing towards this direction, we exploit the parallelization possibilities of modern CPUs in tandem with strong local propagation methods in a novel way. Instead of trying to parallelize constraint propagation algorithms, we propose two search algorithms that apply different propagation methods in parallel. Both algorithms consist of a master search process, which is a typical CP solver, and a number of slave processes, with each one implementing a strong propagation method. The first algorithm runs the different propagators synchronously at each node of the search tree explored in the master process, while the second one can run them asynchronously at different nodes of the search tree. Preliminary experimental results on well-established benchmarks display the promise of our research by illustrating that our algorithms have execution times equal to those of serial solvers, in the worst case, while being faster in most cases.