This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of CSP model and model redundancy, and show how mutually redundant models can be combined and connected using channeling constraints. The combined model contains the mutually redundant models as sub-models. Channeling constraints allow the sub-models to cooperate during constraint solving by propagating constraints freely amongst the sub-models. This extra level of pruning and propagation activities becomes the source of execution speedup. We perform two case studies to evaluate the effectiveness and efficiency of our method. The first case study is based on the simple and well-known n-queens problem, while the second case study applies our method in the design and construction of a real-life ...

Abstract. In an increasing number of domains such as bioinformatics, combinatorial graph problems arise. We propose a novel way to solve these problems, mainly those that can be translated to constrained subgraph finding. Our approach extends constraint programming by introducing CP(Graph), a new computation domain focused on graphs including a new type of variable: graph domain variables as well as constraints over these variables and their propagators. These constraints are subdivided into kernel constraints and additional constraints formulated as networks of kernel constraints. For some of these constraints a dedicated global constraint and its associated propagator are sketched. CP(Graph) is integrated with finite domain and finite sets computation domains, allowing the combining of constraints of these domains with graph constraints. A prototype of CP(Graph) built over finite domains and finite sets in Oz is presented. And we show that a problem of biochemical network analysis can be very simply described and solved within CP(Graph). 1

The Social Golfer Problem has been extensively used in recent years by the constraint community as an example of highly symmetric problem. It is an excellent problem for benchmarking symmetry breaking mechanisms such as SBDS or SBDD and for demonstrating the importance of the choice of the right model for one problem. We address in this paper a specific instance of the Golfer Problem well known as the Kirkman's Schoolgirl Problem and list a collection of techniques and tricks to find efficiently all its unique solutions. In particular, we propose SBDD+, an generic improvement over SBDD which allows a deep pruning when a symmetry is detected during the search. Our implementation of the presented techniques allows us to improve previous published results by an order of magnitude for CPU time as well as number of backtracks, and to compute the seven unique solutions of the Kirkman's problem in a few seconds.

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We report on the extension of the concurrent constraint language Oz by constraints over finite sets of integers. Set constraints are an important addition to the constraint programming system Oz and are very employable in natural language processing and general problem solving. This extension profits much from its integration with the existing constraint systems over finite domains and feature trees, as well as from the availability of first-class procedures. This combination of features is unique to Oz. This paper focuses on the expressiveness gained by set constraints and on the benefits of the integration with finite domain constraints. A number of case studies demonstrates programming techniques exploring these advantages.

In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs. We demonstrate that the ROBDD-based approach provides unprecedented flexibility in modeling constraint satisfaction problems, leading to performance improvements. We also show that the ROBDD-based modeling approach can be extended to the modeling of integer and multiset constraint problems in a straightforward manner. Since domain propagation is not always practical, we also show how to incorporate less strict consistency notions into the ROBDD framework, such as set bounds, cardinality bounds and lexicographic bounds consistency. Finally, we present experimental results that demonstrate the ROBDD-based solver performs better than various more conventional constraint solvers on several standard set constraint problems. 1.

Dominance constraints are widely used in computational linguistics as a language for talking and reasoning about trees. In this paper, we extend dominance constraints by admitting set operators. We present a solver for dominance constraints with set operators, which is based on propagation and distribution rules, and prove its soundness and completeness.

Finite set constraint systems represent a natural choice to model combinatorial configuration problems involving set disjointness, covering or partitioning relations. However, for efficiency reasons, alternative formulations based on Finite Domain or 0-1 integer programming are often preferred even though they require much modelling effort. To offer a better trade-off "natural formulation"/efficiency we propose to improve the efficiency of set constraint solvers by introducing global reasoning on a class of finite set constraints. These are n-ary constraints like atmost1-incommon, distinct upon sets of known cardinality. In this paper we show how the representation of sets within powersets specified as set intervals allows us to derive some global pruning based on mathematical and combinatorial analysis formulas. They improve greatly the filtering enforced by bound consistency methods, and allow to detect failure at early stages. Preliminary results are illustrated on the ternary Steiner and a generic distinct problems. 1

We propose high-level type constructors for constraint programming languages, so that constraint satisfaction problems can be modelled in very expressive ways. We design a practical set constraint language, called ESRA, by incorporating these ideas on top of OPL. A set of rewrite rules achieves compilation from ESRA into OPL, yielding programs that are often very similar to those that a human OPL modeller would (have to) write anyway, so that there is no loss in solving efficiency.

Abstract. In CP literature combinatorial design problems such as sport scheduling, Steiner systems, error-correcting codes and more, are typically solved using Finite Domain (FD) models despite often being more naturally expressed as Finite Set (FS) models. Existing FS solvers have difficulty with such problems as they do not make strong use of the ubiquitous set cardinality information. We investigate a new approach to strengthen the propagation of FS constraints in a tractable way: extending the domain representation to more closely approximate the true domain of a set variable. We show how this approach allows us to reach a stronger level of consistency, compared to standard FS solvers, for arbitrary constraints as well as providing a mechanism for implementing certain symmetry breaking constraints. By experiments on Steiner Systems and error correcting codes, we demonstrate that our approach is not only an improvement over standard FS solvers but also an improvement on recently published results using FD 0/1 matrix models as well. 1