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Optimization of simple tabular reduction for table constraints
 In Proceedings of CP’08
, 2008
"... Abstract. Table constraints play an important role within constraint programming. Recently, many schemes or algorithms have been proposed to propagate table constraints or/and to compress their representation. We show that simple tabular reduction (STR), a technique proposed by J. Ullmann to dynamic ..."
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Abstract. Table constraints play an important role within constraint programming. Recently, many schemes or algorithms have been proposed to propagate table constraints or/and to compress their representation. We show that simple tabular reduction (STR), a technique proposed by J. Ullmann to dynamically maintain the tables of supports, is very often the most efficient practical approach to enforce generalized arc consistency within MAC. We also describe an optimization of STR which allows limiting the number of operations related to validity checking or search of supports. Interestingly enough, this optimization makes STR potentially r times faster where r is the arity of the constraint(s). The results of an extensive experimentation that we have conducted with respect to random and structured instances indicate that the optimized algorithm we propose is usually around twice as fast as the original STR and can be up to one order of magnitude faster than previous stateoftheart algorithms on some series of instances. 1
Abscon 109 A generic CSP solver
"... Abstract. This paper describes the algorithms, heuristics and general strategies used by the two solvers which have been elaborated from the Abscon platform and submitted to the second CSP solver competition. Both solvers maintain generalized arc consistency during search, explore the search space u ..."
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Abstract. This paper describes the algorithms, heuristics and general strategies used by the two solvers which have been elaborated from the Abscon platform and submitted to the second CSP solver competition. Both solvers maintain generalized arc consistency during search, explore the search space using a conflictdirected variable ordering heuristic, integrate nogood recording from restarts and exploit a transposition table approach to prune the search space. At preprocessing, the first solver enforces generalized arc consistency whereas the second one enforces existential SGAC, a partial form of singleton generalized arc consistency. 1
Encoding Table Constraints in CLP(FD) Based on Pairwise AC
"... Abstract. We present an implementation of table constraints in CLP(FD). For binary constraints, the supports of each value are represented as a finitedomain variable, and action rules are used to propagate value exclusions. The bitvector representation of finite domains facilitates constanttime r ..."
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Abstract. We present an implementation of table constraints in CLP(FD). For binary constraints, the supports of each value are represented as a finitedomain variable, and action rules are used to propagate value exclusions. The bitvector representation of finite domains facilitates constanttime removal of unsupported values. For nary constraints, we propose pairwise arc consistency (AC), which ensures that each value has a support in the domain of every related variable. Pairwise AC does not require introducing new problem variables as done in binarization methods and allows for compact representation of constraints. Nevertheless, pairwise AC is weaker than general arc consistency (GAC) in terms of pruning power and requires a final check when a constraint becomes ground. To remedy this weakness, we propose adopting early checks when constraints are sufficiently instantiated. Our experimentation shows that pairwise AC with early checking is as effective as GAC for positive constraints. 1
SecondOrder Consistencies
"... In this paper, we propose a comprehensive study of secondorder consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four basic secondorder consistencies, namely path consistency (PC), ..."
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In this paper, we propose a comprehensive study of secondorder consistencies (i.e., consistencies identifying inconsistent pairs of values) for constraint satisfaction. We build a full picture of the relationships existing between four basic secondorder consistencies, namely path consistency (PC), 3consistency (3C), dual consistency (DC) and 2singleton arc consistency (2SAC), as well as their conservative and strong variants. Interestingly, dual consistency is an original property that can be established by using the outcome of the enforcement of generalized arc consistency (GAC), which makes it rather easy to obtain since constraint solvers typically maintain GAC during search. On binary constraint networks, DC is equivalent to PC, but its restriction to existing constraints, called conservative dual consistency (CDC), is strictly stronger than traditional conservative consistencies derived from path consistency, namely partial path consistency (PPC) and conservative path consistency (CPC). After introducing a general algorithm to enforce strong (C)DC, we present the results of an experimentation over a wide range of benchmarks that demonstrate the interest of (conservative) dual consistency. In particular, we show that enforcing (C)DC before search clearly improves the performance of MAC (the algorithm that maintains GAC during search) on several binary and nonbinary structured problems. 1.
Bitvector Algorithms for Binary Constraint Satisfaction and Subgraph Isomorphism
"... A solution to a binary constraint satisfaction problem is a set of discrete values, one in each of a given set of domains, subject to constraints that allow only prescribed pairs of values in specified pairs of domains. Solutions are sought by backtrack search interleaved with a process that removes ..."
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A solution to a binary constraint satisfaction problem is a set of discrete values, one in each of a given set of domains, subject to constraints that allow only prescribed pairs of values in specified pairs of domains. Solutions are sought by backtrack search interleaved with a process that removes from domains those values that are currently inconsistent with provisional choices already made in the course of search. For each value in a given domain, a bitvector shows which values in another domain are or are not permitted in a solution. Bitvector representation of constraints allows bitparallel, therefore fast, operations for editing domains during search. This article revises and updates bitvector algorithms published in the 1970’s, and introduces focus search, which is a new bitvector algorithm relying more on search and less on domainediting than previous algorithms. Focus search is competitive within a limited family of constraint satisfaction problems. Determination of subgraph isomorphism is a specialized binary constraint satisfaction problem for which bitvector algorithms have been widely used since the 1980’s, particularly for matching molecular structures. This article very substantially updates the author’s 1976 subgraph isomorphism algorithm, and reports experimental results with random and reallife data.
Handling Heterogeneous Constraints in Revision Ordering Heuristics
"... Abstract. Most constraint solvers use the general AC5 scheme [17] to handle constraint propagation. AC5 generalizes the concept of constraint revision. Each constraint type can thus be shipped with its own revision algorithm, with various complexities and performances. Previous papers showed that ..."
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Abstract. Most constraint solvers use the general AC5 scheme [17] to handle constraint propagation. AC5 generalizes the concept of constraint revision. Each constraint type can thus be shipped with its own revision algorithm, with various complexities and performances. Previous papers showed that the order in which constraints are revised have a nonnegligible impact on performances of propagation [20,6,1]. However, most of the ideas presented on these papers are based on the use of homogeneous propagators for binary constraints defined in extension. This paper give ideas to handle heterogeneous constraints in a general revision schedule. 1
Dual Consistency for Nonbinary . . .
"... Dual Consistency (DC) was introduced by Lecoutre, Cardon and Vion in [10, 11]. DC is a novel way of handling Path Consistency (PC), with a simpler definition, and new efficient algorithms and approximations. Interestingly, the new definition may be extended to nonbinary constraint networks (CNs). ..."
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Dual Consistency (DC) was introduced by Lecoutre, Cardon and Vion in [10, 11]. DC is a novel way of handling Path Consistency (PC), with a simpler definition, and new efficient algorithms and approximations. Interestingly, the new definition may be extended to nonbinary constraint networks (CNs). DC is thus a way to generalize PC to any CN, while keeping the initial nonbinary constraints of the CN, and their associated propagators, untouched. DC can also be seen as a simple and efficient way to generate automatically implicit binary constraints. This article presents the implications of this generalization in terms of complexity. Preliminary experimental results shows the potential effectiveness of dynamic implicit constraints generation, as well as identifying its weaknesses. Prospective ideas of approximations, whose purpose is to handle these weaknesses in practice, are then proposed.
“Evaluation and optimization of innovative production systems of goods and services” A NEW METHOD TO SOLVE AND OPTIMIZE MILITARY FAP WITH NARY CONSTRAINTS
"... ABSTRACT: The problem considered in this paper consists in defining an assignment of frequencies to radio links between transmitters and receivers in order to minimize the global interference inside the network. This problem can be modeled as a CSP (Constraint Satisfaction Problem). It is classified ..."
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ABSTRACT: The problem considered in this paper consists in defining an assignment of frequencies to radio links between transmitters and receivers in order to minimize the global interference inside the network. This problem can be modeled as a CSP (Constraint Satisfaction Problem). It is classified as NPhard problem. Numerous studies have reported various methods to solve this problem optimally and many results have been presented. We applied, to this version of the frequency assignment problem, an original hybrid method that combines constraint propagation techniques and Tabu search. The method is based on finding and storing the variable/value associations that lead to infeasible solutions. It allows the algorithm to dynamically manage the cuts of branches and the access to the decision variables. It is a learning system that progressively extends the algorithm knowledge on the problem and increases its effectiveness. Computational results obtained on a number of standard problem instances prove the effectiveness of the proposed approach.