A lazy divide and conquer approach to constraint solving

Abstract

A divide and conquer strategy enables a problem to be divided into subproblems, which are solved independently and later combined to form solutions of the original problem. For solving constraint satisfaction problems, however, the divide and conquer technique has not been shown to be effective. This is because it is not possible to cleanly divide a problem into independent subproblems in the presence of constraints that involve variables belonging to different subproblems. Consequently, solutions of one subproblem may prune solutions of another subproblem, making those solutions of the latter subproblem redundant. In this paper we propose a divide and conquer approach to constraint solving in a lazy evaluation framework. In this framework, a subproblem is solved on demand, which eliminates redundant consistency checks. Moreover, once solved, the solutions of a subproblem can be reused in the satisfaction of various global constraints connecting this subproblem with others, thus reducing the search space. We also demonstrate the effectiveness of our algorithm in solving a practical problem: finding all instances of a user-defined pattern in stock market price charts.