Abstract. Call control features (e.g., call-divert, voice-mail) are primitive options to which users can subscribe off-line to personalise their service. The configuration of a feature subscription involves choosing and sequencing features from a catalogue and is subject to constraints that prevent undesirable feature interactions at run-time. When the subscription requested by a user is inconsistent, one problem is to find an optimal relaxation. In this paper, we show that this problem is NP-hard and we present a constraint programming formulation using the variable weighted constraint satisfaction problem framework. We also present simple formulations using partial weighted maximum satisfiability and integer linear programming. We experimentally compare our formulations of the different approaches; the results suggest that our constraint programming approach is the best of the three overall. 1

Abstract. This work concentrates on improving the robustness of constraint solvers by increasing the propagation strength of constraint models in a declarative and automatic manner. Our objective is to efficiently identify and remove shavable values during search. A value is shavable if as soon as it is assigned to its associated variable an inconsistency can be detected, making it possible to refute it. We extend previous work on shaving by using different techniques to decide if a given value is an interesting candidate for the shaving process. More precisely, we exploit the semantics of (global) constraints to suggest values, and reuse both the successes and failures of shaving later in search to tune shaving further. We illustrate our approach with two important global constraints, namely alldifferent and sum, and present the results of an experimentation obtained for three problem classes. The experimental results are quite encouraging: we are able to significantly reduce the number of search nodes (even by more than two orders of magnitude), and improve the average execution time by one order of magnitude. 1

Abstract. This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to event-based constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different levels of consistency for different subsets of constraints in the same model. Moreover, we show how strong consistencies can be applied with different kinds of constraints, including user-defined constraints. We experiment our technique with a coarse-grained algorithm for Max-RPC, called Max-RPC rm and a variant of it, L-Max-RPC rm. Experiments confirm the interest of strong consistencies for Constraint Programming tools. 1

Abstract. This article presents a generic scheme for adding strong local consistencies to the set of features of constraint solvers, which is notably applicable to event-based constraint solvers. We encapsulate a subset of constraints into a global constraint. This approach allows a solver to use different levels of consistency for different subsets of constraints in the same model. Moreover, we show how strong consistencies can be applied with different kinds of constraints, including user-defined constraints. We experiment our technique with a coarse-grained algorithm for Max-RPC, called Max-RPC rm, and a variant of it, L-Max-RPC rm. Experiments confirm the interest of strong consistencies for Constraint Programming tools. 1

Abstract. In constraint satisfaction, basic inferences rely on some properties of constraint networks, called consistencies, that allow the identification of inconsistent instantiations (also called nogoods). Two main families of consistencies have been introduced so far: those that permit us to reason from variables such as (i, j)-consistency and those that permit us to reason from constraints such as relational (i, j)-consistency. This paper introduces a new family of consistencies based on the concept of failed value (a value pruned during search). This family is orthogonal to previous ones. 1

In this paper, we propose a new algorithm for enforcing relational consistency on every set of k constraints of a finite Constraint Satisfaction Problem (CSP). This algorithm operates by filtering the constraint while leaving the topology of the graph unchanged. We study the resulting relational consistency property and compare it to existing ones. We evaluate the effectiveness of our algorithm in a search procedure for solving CSPs and demonstrate the applicability, effectiveness, and usefulness of enforcing high levels of consistency. 1.

Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. For non-binary Constraint Satisfaction Problems (CSPs), the relational-consistency property R(i,j)C of [Dechter and van Beek 1997] may add new non-binary constraints to the constraint network, thus modifying its topology. The domain-filtering properties of [Bessière et al. 2008] filter the domains of the variables and leave the constraints unchanged but are restricted to combinations of two constraints. We restate the property of m-wise consistency [Gyssens 1986; Jégou 1993] as relational (∗,m)-consistency, R(∗,m)C. R(∗,m)C ensures that any tuple in a relation is consistent in every combination of m constraints. The main contributions of this document are the design of an algorithm for enforcing R(∗,m)C and the evaluation of its effectiveness in a search procedure solving CSPs. This document thus establishes the usefulness in practice of higher consistency

Call control features (e.g., call-divert, voice-mail) are primitive options to which users can subscribe off-line to personalise their service. The configuration of a feature subscription involves choosing and sequencing features from a catalogue and is subject to constraints that prevent undesirable feature interactions at run-time. When the subscription requested by a user is inconsistent, one problem is to find an optimal relaxation, which is a generalisation of the feedback vertex set problem on directed graphs, and thus it is an NP-hard task. We present several constraint programming formulations of the problem. We also present formulations using partial weighted maximum Boolean satisfiability and mixed integer linear programming. We study all these formulations by experimentally comparing them on a variety of randomly generated instances of the feature subscription problem. 1.