Parallel Arc-Consistency for Functional Constraints

We present in this paper a parallel execution model of arc-consistency for Constraint Satisfaction Problems (CSP), implemented on a scaleable MIMD distributed memory machine. We have adopted the indexical scheme, an adequate approach to arc-consistency for functional constraints. The CSP is partitioned into N partitions, which are executed in parallel on N processors. Each processor applies sequential arc-consistency to its subset of constraints, updating remote domains of variables shared by any other processor. The parallel algorithm we propose is embedded in the constraint solver PCSOS (Parallel Constraint Satisfaction and Optimisation System). PCSOS invokes the parallel arc-consistency algorithm when performing labelling to obtain the solutions of a CSP. PCSOS is written in C, and it has been developed and tested on a CRAY T3E distributed memory multiprocessor with up to twenty-six processors. Results on speedup and behaviour of the system are reported for the search of the rst solution of diierent CSPs.