Finite Domain Constraint Programming Systems

Schulte, Christian; Carlsson, Mats

doi:10.1016/s1574-6526(06)80018-0

Cited by 28 publications

(24 citation statements)

References 15 publications

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“…Schulte and Smolka (2004) illustrate on the 3-fractions puzzle the advantages of using redundant constraints implied by a symmetry breaking rule (the fractions are sorted in non-decreasing order). Frisch et al (2001) use proof planning to generate implied algebraic constraints that improve the solution of the previous model.…”

Section: Informs Transactions On Educationmentioning

confidence: 99%

Puzzle—Solving the n-Fractions Puzzle as a Constraint Programming Problem

Malapert

Provillard

2018

INFORMS Transactions on Education

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Abstract. The aim in solving puzzles is to find the solution using several clues and restrictions. In this paper, we solve a numerical puzzle, the n-fractions puzzle, by constraint programming. The n-fractions puzzle is problem 41 of the CSPLib, a library of test problems for constraint solvers. Models referenced in the CSPLib return invalid solutions as soon as the number n of fractions exceeds five. To solve the n-fractions puzzle, we first provide an upper bound for the unsatisfiability inspired by constraint filtering techniques. Then we propose two new constraint programming models that exploit the integer factorization of the fractions' denominators and their lowest common multiple. The proposed models can solve up to the 19-fractions puzzle within a few minutes and without returning invalid solutions. Some restrictions of the models that eliminate invalid solutions still allow them to solve larger n-fractions puzzles, even if the solving times increase. At the end, only six n-fractions puzzles remain open.

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Section: Informs Transactions On Educationmentioning

confidence: 99%

Puzzle—Solving the n-Fractions Puzzle as a Constraint Programming Problem

Malapert

Provillard

2018

INFORMS Transactions on Education

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“…The same operations in a range sequence that has been implemented as a linked list [7] require O(δ) steps, while the space complexity is much less (O(δ) too) than the bit vector's one (O(d)). A wiser choice would be to implement the range sequence as a binary search tree, with an average search/removal complexity O(log δ), and the space complexity left unaffected.…”

Section: Efficient Domain Implementationsmentioning

confidence: 99%

“…To the best of our knowledge, the representation of a domain itself has not yet been the primary sector of interest of a specific publication in the area. Nevertheless, Schulte and Carlsson in their Constraint Programming systems survey [7] defined formally the two most popular data structures that can represent a finite set of integers: [11].…”

Section: Introductionmentioning

confidence: 99%

Flexible Management of Large-Scale Integer Domains in CSPs

Pothitos

Stamatopoulos

2010

Artificial Intelligence: Theories, Models and Applications

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Abstract. Most research on Constraint Programming concerns the (exponential) search space of Constraint Satisfaction Problems (CSPs) and intelligent algorithms that reduce and explore it. This work proposes a different way, not of solving a problem, but of storing the domains of its variables, an important-and less focused-issue especially when they are large. The new data structures that are used are proved theoretically and empirically to adapt better to large domains, than the commonly used ones. The experiments of this work display the contrast between the most popular Constraint Programming systems and a new system that uses the data structures proposed in order to solve CSP instances with wide domains, such as known Bioinformatics problems.

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“…Figure 1 describes a classic constraint propagation engine [10]. In this algorithm, constraints are managed as propagators 1 in a propagation queue, Q.…”

Section: Definition 21 a Constraint Satisfaction Problem (Csp) Is Amentioning

confidence: 99%

Exploiting weak dependencies in tree-based search

Arbeláez

Hamadi

2009

Proceedings of the 2009 ACM Symposium on Applied Computing

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In this work, our objective is to heuristically discover a simplified form of functional dependencies between variables called weak dependencies. Once discovered, these relations are used to rank the variables. Our method shows that these relations can be detected with some acceptable overhead during constraint propagation. More precisely, each time a variable y gets instantiated as a result of the instantiation of x, a weak dependency (x, y) is recorded. As a consequence, the weight of x is raised, and the variable becomes more likely to be selected by the variable ordering heuristic. Experiments on a large set of problems show that on the average, the search trees are reduced by a factor 3 while runtime is decreased by 31% when compared against dom-wdeg, one of the best dynamic variable ordering heuristic.

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Finite Domain Constraint Programming Systems

Cited by 28 publications

References 15 publications

Puzzle—Solving the n-Fractions Puzzle as a Constraint Programming Problem

Puzzle—Solving the n-Fractions Puzzle as a Constraint Programming Problem

Flexible Management of Large-Scale Integer Domains in CSPs

Exploiting weak dependencies in tree-based search

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