Propagating Soft Table Constraints

Abstract

Abstract. WCSP is a framework that has attracted a lot of attention during the last decade. In particular, many filtering approaches have been developed on the concept of equivalence-preserving transformations (cost transfer operations), using the definition of soft local consistencies such as, for example, node consistency, arc consistency, full directional arc consistency, and existential directional arc consistency. Almost all algorithms related to these properties have been introduced for binary weighted constraint networks, and most of the conducted experiments typically include networks with binary and ternary constraints only. In this paper, we focus on extensional soft constraints (of large arity), so-called soft table constraints. We propose an algorithm to enforce a soft version of generalized arc consistency (GAC) on such constraints, by combining both the techniques of cost transfer and simple tabular reduction, the latter dynamically maintaining the list of allowed tuples in constraint tables. On various series of problem instances containing soft table constraints of large arity, we show the practical interest of our approach.

Solving WCSP by Extraction of Minimal Unsatisfiable Cores

“…In this paper, we focus on extensional soft constraints. These are soft table constraints where some tuples are explicitly listed with their costs in a table, and a default cost indicates the cost of all implicit tuples (i.e., those not present in the table) ; e.g., see [15]. Below, we introduce both the notions of layer and front.…”