Constructive Cardinality

We describe a set of necessary conditions that are useful for generating propagation algorithms for the cardinality operator as well as for over-constrained problems with preferences. Constructive disjunction as well as the entailments rules originally proposed for the cardinality operator can be seen as simple cases of these necessary conditions. In addition these necessary conditions have the advantage of providing more pruning

Multiplex dispensation order generation for pyrosequencing

This paper introduces the multiplex dispensation order generation problem, a real-life combinatorial problem that arises in the context of analyzing large numbers of short to medium length DNA sequences. The problem is modeled as a constraint optimization problem (COP). We present the COP, its constraint programming formulation, and a custom search procedure. We give some experimental data supporting our design decisions. One of the lessons learnt from this study is that the ease with which the relevant constraints are expressed can be a crucial factor in making design decisions in the COP model

Synchronized sweep algorithms for scalable scheduling constraints

This report introduces a family of synchronized sweep based filtering algorithms for handling scheduling problems involving resource and precedence constraints. The key idea is to filter all constraints of a scheduling problem in a synchronized way in order to scale better. In addition to normal filtering mode, the algorithms can run in greedy mode, in which case they perform a greedy assignment of start and end times. The filtering mode achieves a significant speed-up over the decomposition into independent cumulative and precedence constraints, while the greedy mode can handle up to 1 million tasks with 64 resources constraints and 2 million precedences. These algorithms were implemented in both CHOCO and SICStus

Tracing and Explaining Execution of CLP(FD) Programs

Previous work in the area of tracing CLP(FD) programs mainly focuses on providing information about control of execution and domain modification. In this paper, we present a trace structure that provides information about additional important aspects. We incorporate explanations in the trace structure, i.e. reasons for why certain solver actions occur. Furthermore, we come up with a format for describing the execution of the filtering algorithms of global constraints. Some new ideas about the design of the trace are also presented. For example, we have modeled our trace as a nested block structure in order to achieve a hierarchical view. Also, new ways about how to represent and identify different entities such as constraints and domain variables are presented.Comment: 16 pages; Alexandre Tessier, editor; WLPE 2002, http://xxx.lanl.gov/abs/cs.SE/020705

Global constraints as graph properties on structured network of elementary constraints of the same type

This report introduces a classification scheme for the global constraints. This classification is based on four basic ingredients from which one can generate almost all existing global constraints and come up with new interesting constraints. Global constraints are defined in a very concise way, in term of graph properties that have to hold, where the graph is a structured network of same elementary constraints. Since this classification is based on the internal structure of the global constraints it is also a strong hint for the pruning algorithms of the global constraints

Propagating Regular Counting Constraints

Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. Moreover, the wide variety of such constraints in practical applications led to general modelling techniques and generic propagation algorithms, often based on deterministic finite automata (DFA) and their extensions. We consider counter-DFAs (cDFA), which provide concise models for regular counting constraints, that is constraints over the number of times a regular-language pattern occurs in a sequence. We show how to enforce domain consistency in polynomial time for atmost and atleast regular counting constraints based on the frequent case of a cDFA with only accepting states and a single counter that can be incremented by transitions. We also prove that the satisfaction of exact regular counting constraints is NP-hard and indicate that an incomplete algorithm for exact regular counting constraints is faster and provides more pruning than the existing propagator from [3]. Regular counting constraints are closely related to the CostRegular constraint but contribute both a natural abstraction and some computational advantages.Comment: Includes a SICStus Prolog source file with the propagato

A geometric constraint over k-dimensional objects and shapes subject to business rules

This report presents a global constraint that enforces rules written in a language based on arithmetic and first-order logic to hold among a set of objects. In a first step, the rules are rewritten to Quantifier-Free Presburger Arithmetic (QFPA) formulas. Secondly, such formulas are compiled to generators of k-dimensional forbidden sets. Such generators are a generalization of the indexicals of cc(FD). Finally, the forbidden sets generated by such indexicals are aggregated by a sweep-based algorithm and used for filtering. The business rules allow to express a great variety of packing and placement constraints, while admitting efficient and effective filtering of the domain variables of the k-dimensional object, without the need to use spatial data structures. The constraint was used to directly encode the packing knowledge of a major car manufacturer and tested on a set of real packing problems under these rules, as well as on a packing-unpacking problem

Une contrainte cumulative continue multi-ressources avec des conso mmations - Productions en ressources Positives - Négatives

Cet article introduit une extension de la contrainte cumulative classique : une tâche n'est plus représentée par un simple rectangle mais par une suite de sous-tâches trapézoïdales de durées et hauteurs variables. La fonction de ressource n'est plus une constante, mais une fonction du temps, linéaire par morceaux, positive ou négative. Enfin, unetâche n'est pas pré-affectée à une ressource mais à une tâche correspond un ensemble d'affectations possibles. Dans ce contexte, cet article propose un algorithme en $O(p \cdot (\log p +q))$ pour calculer les profils minimum etmaximum d'utilisation des ressources par les tâches où $q$ est le nombre de ressources et $p$ le nombre total de sous-tâches de toutes les tâches

Condition nécessaire pour la contrainte de partitionnement de graphes par des chemins

Etant donné un graphe orienté \cG, le problème des \NPATH-chemins disjoints consiste à trouver une partition de \cG en \NPATH chemins noeuds-disjoints, tel que chaque chemin termine sur un noeud appartenant à un sous-ensemble des noeuds de \cG. Cet article fournit une condition nécessaire, pour le problème des \NPATH-chemins disjoints, combinant (1) la structure du graphe réduit associé au graphe \cG, (2) la structure de chaque composante fortement connexe de \cG vis à vis des relations de dominance entre les noeuds de \cG, et (3) la structure des connexions entre les composantes fortement connexes de \cG. Finalement, nous montrons comment exploiter cette condition nécessaire pour en dériver une contrainte de partitionnement de graphes par des chemins

On the Reification of Global Constraints

We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on the observation that most global constraints can be reformulated as a conjunction of pure functional dependency constraints together with a constraint that can be easily reified. We first show how the core constraints of the Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at least 82% of the constraints in the Global Constraint Catalogue