Concurrently Decomposable Constraint Systems

Abstract. In constraint satisfaction, decomposition is a common technique to split a problem in a number of parts in such a way that the global solution can be efficiently assembled from the solutions of the parts. In this paper, we study the decomposition problem from an autonomous agent perspective. Here, a con-straint problem has to be solved by different agents each controlling a disjoint set of variables. Such a problem is called concurrently decomposable if each agent is (i) capable to solve its own part of the problem independently of the others, and (ii) the individual solutions always can be merged to a complete solution of the total problem. First of all, we investigate how difficult it is to decide whether or not a given constraint system and agent partitioning allows for such a concur-rent decomposition. Secondly, we investigate how difficult it is to find suitable reformulations of the original constraint problem that allow for concurrent de-composition.