Parallel execution models for constraint programming over finite domains

Abstract

Many problems from artificial intelligence can be described as constraint satisfaction problems over finite domains (CSP(FD)), that is, a solution is an assignment of a value from a finite domain to each problem variable such that a set of constraints is satisfied. Arc-consistency algorithms remove inconsistent values from the set of values that can be assigned to a variable (its domain), thus reducing the search space. We have developed two parallelisation models of arc-consistency to be run on MIMD multiprocessors. Two different policies, static and dynamic, to schedule the execution of constraints have been tested. In the static scheduling policy, the set of constraints is divided into N partitions, which are executed in parallel on N processors. We discuss an important factor affecting performance, the criterion to establish the partition in order to balance the run-time workload. In the dynamic scheduling policy, any processor can execute any constraint, improving the workload balance. However, a coordination mechanism is required to ensure a sound order in the execution of constraints. Both parallelisation models have been implemented on a CRAY T3E multiprocessor with up to thirty four processors. Empirical results on speedup and behaviour of both models are reported and discussed.