Ways of Maintaining Arc Consistency in Search Using the Cartesian Representation

Abstract

Abstract. The search space of constraint satisfaction problems (CSPs) can be reduced by using value interchangeability. This notion consists of aggregating subsets of values that behave similarly on the future branches of the search. , is a typical backtracking algorithm using value interchangeability. It uses the Cartesian product representation of the search space (CPR) which aggregates partial solutions and proves particularly useful for finding and representing all solutions of a CSP. It is assessed that maintaining arc-consistency (MAC) is the most efficient general algorithm for solving hard problems. A few work on combining MAC with CPR exists. In this paper we study comparatively two other possible alternatives of MAC-CPR.

Distributed asynchronous search with private constraints (extended abstract)

“…In the current implementation, the aggregation mechanism guarantees a complete and non-redundant covering of the search space determined by the local constraints [1]. Variants such as the ones mentioned in [2] can also be considered. In fact, AAS can be understood as a dynamic set of parallel AS, synchronized with each other and operating on the dual constraint graph, where the variables are relations of the original problem and the relations ensure that identical variables take on identical assignments.…”

“…Thus, A z maintains value combinations for xz and .T3, A 2 for xl and x2, A 3 for xl and x3, and A 4 for all of x2, x3 and x4. AAS works like AS, but differs in the fact that message arguments are not just individual assignments, but Cartesian products of assignments [2] to different variables. More precisely, in the current implementation of AAS, an assignment is a list of intervals, one for each involved variable, which compactly represent all the tuples of their Cartesian product.…”