Improving domain filtering using restricted path consistency

Abstract

This paper introduces a new level of partial consistency for constraint satisfaction problems, which is situated between arc and path-consistency. We call this level restricted path-consistency (RPC). Two procedures to enforce complete and partial RPC are presented. They both use path-based verifications to detect inconsistencies but retain the good features of arcconsistency since they only touch the variables domains and do not augment the connectivity of the constraint graph. We show that, although they perform a limited number of checks, these procedures exhibit a considerable pruning power.

New algorithms for max restricted path consistency

“…More details about these instances can be found in C.Lecoutre's homepage. 4 All algorithms used the dom/wdeg heuristic for variable ordering [12] and lexicographic value ordering. As explained in Section 2, dom/wdeg increases the weight of a constraint when this constraint causes a value removal.…”

“…Domain filtering consistencies are especially interesting because they only filter values from domains and as a result they do not alter either the constraint graph by adding new constraints, or the constraints' relations by removing inconsistent tuples [15]. Examples of domain filtering consistencies for binary constraints include restricted path consistency [4], path inverse consistency and neighborhood inverse consistency [16], max restricted path consistency [14], and singleton arc consistency [15]. The most famous local consistency that is not cast as domain filtering is path consistency.…”

“…maxRPC was introduced in [14] as an extension to Restricted Path Consistency (RPC). A binary CSP is RPC iff it is AC and for each constraint c i, j and each value a i ∈ D(x i ) that has a single AC-support a j ∈ D(x j ), the pair of values (a i , a j ) is path consistent (PC) [4]. A pair of values (a i , a j ) is PC iff for any third variable x k there exists a value a k ∈ D(x k ) s.t.…”

Constraint Propagation

“…They all deal with 'triangles' of constraints, namely triples of variables connected two-by-two by binary constraints. The first local consistency following this line of research is Restricted Path Consistency (RPC), proposed by Berlandier [13]. The motivation for RPC is to remove more inconsistent values than arc consistency whereas avoiding the cost of path consistency.…”

Domain Filtering Consistencies

“…Restricted path consistency The aim of Berlandier when he proposed restricted path consistency (RPC, Berlandier, 1995) was to remove more inconsistent values than AC while avoiding the drawbacks of path consistency. Even the most e cient PC algorithms have to try to extend all the pairs of values (even those between two variables that are not neighbors) to any third variable.…”