Intermediary Local Consistencies

International audienceWe propose a new definition for characterizing levels of consistency. A perspective is to provide new tools for classifying filtering algorithms, including incomplete algorithms based on the semantics of constraints

Intermediary Local Consistencies

International audienceWe propose a new definition for characterizing levels of consistency. A perspective is to provide new tools for classifying filtering algorithms, including incomplete algorithms based on the semantics of constraints

Learning parameters for the sequence constraint from solutions

This paper studies the problem of learning parameters for global constraints such as Sequence from a small set of positive examples. The proposed technique computes the probability of observing a given constraint in a random solution. This probability is used to select the more likely constraint in a list of candidates. The learning method can be applied to both soft and hard constraint

Counting solutions of knapsack constraints.

Abstract. This paper furthers the recent investigation of search heuristics based on solution counting information, by proposing and evaluating algorithms to compute solution densities of variable-value pairs in knapsack constraints. Given a domain consistent constraint, our first algorithm is inspired from what was proposed for regular language membership constraints. Given a bounds consistent constraint, our second algorithm draws from discrete uniform distributions. Experiments on several problems reveal that simple search heuristics built from the information obtained by these algorithms can be very effective

Solution Counting for CSP and SAT with Large Tree-Width

Рассмотрена проблема подсчета количества решений задачи совместимости ограничений (Constraint Satisfaction Problem). Для ее решения был адаптирован метод обратного прослеживания с ацикличным представлением графа ограничений (Backtracking with Tree-Decomposition). Предложен точный алгоритм, сложность которого экспоненциально зависит от ширины дерева, и приближенный алгоритм, экспоненциально зависящий от размера максимальной клики.The problem of counting the number of solutions of a CSP is considered. For solving the problem the Backtracking with a Tree-Decomposition method was adapted. The exact algorithm is suggested which has the worst-time complexity exponential in a tree width, as well as iterative algorithm that has computational complexity exponential in a maximum clique size.Розглянуто проблему підрахунку кількості розв’язків задачі сумісності обмежень (Constraint Satisfaction Problem). Для її розв’язку було адаптовано метод зворотного простеження з ациклічним поданням графа обмежень (Backtracking with Tree-Decomposition). Запропоновано точний алгоритм, складність якого експоненційно залежить від ширини дерева, і наближений алгоритм, експоненційно залежний від розміру максимальної кліки

Solution counting algorithms for constraint-centered search heuristics

Constraints have played a central role in cp because they capture key substructures of a problem and efficiently exploit them to boost inference. This paper intends to do the same thing for search, proposing constraint-centered heuristics which guide the exploration of the search space toward areas that are likely to contain a high number of solutions. We first propose new search heuristics based on solution counting information at the level of individual constraints. We then describe efficient algorithms to evaluate the number of solutions of two important families of constraints: occurrence counting constraints, such as alldifferent, and sequencing constraints, such as regular. Inboth cases we take advantage of existing filtering algorithms to speed up the evaluation. Experimental results on benchmark problems show the effectiveness of our approach

Solution Counting Algorithms for Constraint-Centered Search Heuristics

Constraints have played a central role in cp because they capture key substructures of a problem and efficiently exploit them to boost inference. This paper intends to do the same thing for search, proposing constraint-centered heuristics which guide the exploration of the search space toward areas that are likely to contain a high number of solutions. We first propose new search heuristics based on solution counting information at the level of individual constraints. We then describe efficient algorithms to evaluate the number of solutions of two important families of constraints: occurrence counting constraints, such as alldifferent, and sequencing constraints, such as regular. In both cases we take advantage of existing filtering algorithms to speed up the evaluation. Experimental results on benchmark problems show the effectiveness of our approach