Data-Parallel Design of an Interval-Based Constraint Language: Analysis of Speed-Ups

Abstract

This paper presents what is believed to be the very first design and implementation of a deterministic data-parallel constraint language based on interval variables (integer or floating point intervals). The approach used consists of having one constraint and one interval variable per processor. Each processor narrows and intersects the constraint it stores within its memory using interval variables which are stored in different processors. Whenever a solution is found, it is printed and the processor is re-used in implementing the splitting operation. Similarly, a failed narrowing or intersection frees the corresponding processor to be re-used in a subsequent split operation. The algorithm starts with an initial set of processors corresponding to the constraints to be solved and their variables. Narrowing and intersections are applied until convergence. Splitting is done by selecting the variable with the smallest interval and introducing a new set of processors whose data is copied ..