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Theory and practice of constraint propagation
 In Proceedings of the 3rd Workshop on Constraint Programming in Decision and Control
, 2001
"... Abstract: Despite successful application of constraint programming (CP) to solving many reallife problems there is still an indispensable group or researchers considering (wrongly) CP as a simple evaluation technique only. Even if sophisticated search algorithms play an important role in solving co ..."
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Cited by 17 (1 self)
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Abstract: Despite successful application of constraint programming (CP) to solving many reallife problems there is still an indispensable group or researchers considering (wrongly) CP as a simple evaluation technique only. Even if sophisticated search algorithms play an important role in solving constraintbased models, the real power engine behind CP is called constraint propagation (domain filtering, pruning or consistency techniques). In the paper we give a survey of common consistency techniques for binary constraints. We describe the main ideas behind them, list their advantages and limitations, and compare their pruning power. Then we briefly explain how these techniques can be extended to nonbinary constraints. Last part of the paper is devoted to modelling issues. We give some hints how the constraint propagation can be exploited more when solving reallife problems. This part is based on our experience with solving reallife programs and it is also supported by empirical observations of other researchers.
SAT v CSP
 PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING (CP00)
, 2000
"... We perform a comprehensive study of mappings between constraint satisfaction problems (CSPs) and propositional satisfiability (SAT). We analyse four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, we compare the impact of achieving arcconsistency o ..."
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Cited by 16 (1 self)
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We perform a comprehensive study of mappings between constraint satisfaction problems (CSPs) and propositional satisfiability (SAT). We analyse four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, we compare the impact of achieving arcconsistency on the CSP with unit propagation on the SAT problem. We then extend these results to CSP algorithms that maintain (some level of) arcconsistency during search like FC and MAC, and to the DavisPutnam procedure (which performs unit propagation at each search node). Because of differences in the branching structure of their search, a result showing the dominance of achieving arcconsistency on the CSP over unit propagation on the SAT problem does not necessarily translate to the dominance of MAC over the DavisPutnam procedure. These results provide insight into the relationship between propositional satisfiability and constraint satisfaction.
Decomposable Constraints
, 2000
"... Many constraint satisfaction problems can be naturally and efficiently modelled using nonbinary constraints like the "alldifferent" and "global cardinality" constraints. Certain classes of these nonbinary constraints are "network decomposable" as they can be represented by binary constraints ..."
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Cited by 16 (3 self)
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Many constraint satisfaction problems can be naturally and efficiently modelled using nonbinary constraints like the "alldifferent" and "global cardinality" constraints. Certain classes of these nonbinary constraints are "network decomposable" as they can be represented by binary constraints on the same set of variables. We compare theoretically the levels of consistency which are achieved on nonbinary constraints to those achieved on their binary decomposition. We present many new results about the level of consistency achieved by the forward checking algorithm and its various generalizations to nonbinary constraints. We also compare the level of consistency achieved by arcconsistency and its generalization to nonbinary constraints, and identify special cases of nonbinary decomposable constraints where weaker or stronger conditions, than in the general case, hold. We also analyze the cost, in consistency checks, required to achieve certain levels of consistency.
Extending forward checking
 in Proceedings of CP’00
, 2000
"... Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from ..."
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Cited by 16 (4 self)
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Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from the domains of the uninstantiated variables. In this paper we present a general approach to extending constraint propagating algorithms, especially forward checking. In particular, we provide a simple yet flexible mechanism for pruning domain values, and show that with this in place it becomes easy to utilize new mechanisms for detecting inconsistent values during search. This leads to a powerful and uniform technique for designing new CSP algorithms: one simply need design new methods for detecting inconsistent values and then interface them with the domain pruning mechanism. Furthermore, we also show that algorithms following this design can proved to be correct in a simple and uniform way. To demonstrate the utility of these ideas five “new ” CSP algorithms are presented. 1
A comparison of distributed constraint satisfaction approaches with respect to privacy
 In DCR
, 2002
"... There is an increasing interest in distributed and asynchronous search algorithms for solving distributed constraint satisfaction problems (DisCSP). An important motivation for distributed problem solving is the agents ’ ability to keep their constraints private. Cryptographic techniques [GB96] offe ..."
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Cited by 15 (1 self)
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There is an increasing interest in distributed and asynchronous search algorithms for solving distributed constraint satisfaction problems (DisCSP). An important motivation for distributed problem solving is the agents ’ ability to keep their constraints private. Cryptographic techniques [GB96] offer a certain protection from several types of attacks. However, when an attack succeeds, no agent can know how much privacy he has lost. We assume that agents enforce their privacy by dropping out of the search process whenever the estimated value of the information that they need to reveal in the future exceeds that attached to a successful solution of the DisCSP. We compare several distributed search algorithms as to how likely they are to terminate prematurely for privacy reasons, and arrange the algorithms in a hierarchy that reflects this relation. 1.
Constraint models for the covering test problem
 Constraints
, 2004
"... Abstract. Covering arrays can be applied to the testing of software, hardware and advanced materials, and to the effects of hormone interaction on gene expression. In this paper we develop constraint programming models of the problem of finding an optimal covering array. Our models exploit global co ..."
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Cited by 14 (1 self)
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Abstract. Covering arrays can be applied to the testing of software, hardware and advanced materials, and to the effects of hormone interaction on gene expression. In this paper we develop constraint programming models of the problem of finding an optimal covering array. Our models exploit global constraints, multiple viewpoints and symmetrybreaking constraints. We show that compound variables, representing tuples of variables in our original model, allow the constraints of this problem to be represented more easily and hence propagate better. With our best integrated model, we are able to either prove the optimality of existing bounds or find new optimal solutions, for arrays of moderate size. Local search on a SATencoding of the model is able to find improved solutions and bounds for larger problems. 1
A Dual Graph Translation of a Problem in `Life'
, 2002
"... Conway's game of Life provides interesting problems in which modelling issues in constraint programming can be explored. The problem of finding a maximum density stable pattern (`stilllife') is discussed. A formulation of this problem as a constraint satisfaction problem with 01 variables and non ..."
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Cited by 13 (1 self)
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Conway's game of Life provides interesting problems in which modelling issues in constraint programming can be explored. The problem of finding a maximum density stable pattern (`stilllife') is discussed. A formulation of this problem as a constraint satisfaction problem with 01 variables and nonbinary constraints is compared with its dual graph translation into a binary CSP. The success of the dual translation is surprising, from previouslyreported experience, since it has as many variables as the nonbinary CSP and very large domains. An important factor is the identification of many redundant constraints: it is shown that these can safely be removed from a dual graph translation if arc consistency is maintained during search. 1
Accelerating random walks
 In Proc. 8th Intl. Conf. on the Princ. and Practice of Constraint Programming (CP2002
, 2002
"... Abstract. In recent years, there has been much research on local search techniques for solving constraint satisfaction problems, including Boolean satisfiability problems. Some of the most successful procedures combine a form of random walk with a greedy bias. These procedures are quite effective in ..."
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Cited by 12 (2 self)
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Abstract. In recent years, there has been much research on local search techniques for solving constraint satisfaction problems, including Boolean satisfiability problems. Some of the most successful procedures combine a form of random walk with a greedy bias. These procedures are quite effective in a number of problem domains, for example, constraintbased planning and scheduling, graph coloring, and hard random problem instances. However, in other structured domains, backtrackstyle procedures are often more effective. We introduce a technique that leads to significant speedups of random walk style procedures on structured problem domains. Our method identifies long range dependencies among variables in the underlying problem instance. Such dependencies are made explicit by adding new problem constraints. These new constraints can be derived efficiently, and, literally, “accelerate ” the Random Walk search process. We provide a formal analysis of our approach and an empirical validation on a recent benchmark collection of hardware verification problems. 1
NonBinary Constraints
, 1999
"... Since the origins of the constraint satisfaction paradigm, its restriction to binary constraints has concentrated a significant part of the work. This is understandable because new ideas/techniques are usually much simpler to present/elaborate by first restricting them to the binary case. (See for e ..."
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Cited by 10 (1 self)
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Since the origins of the constraint satisfaction paradigm, its restriction to binary constraints has concentrated a significant part of the work. This is understandable because new ideas/techniques are usually much simpler to present/elaborate by first restricting them to the binary case. (See for example the arc consistency algorithms, such as AC3 or AC4, which have been presented first in their binary version [10, 12], before being extended to nonbinary constraints [11, 13].) But this inclination has highly increased in the early nineties. Authors indeed justied this restriction by the fact that any nonbinary constraint network can polyniomally be converted into an equivalent binary one [6, 8, 5, 19]. And, in most cases, they never extended their work to nonbinary constraints. Up to now, constraint reasoning has generated robust formal definitions (local consistencies, etc.), original resolution methods (filtering, lookback schemes, decomposition techniques, heuristics, etc.), and theo...
Constraint Modeling and Reformulation in the Context Of Academic Task Assignment
 In Working Notes of the Workshop on Modelling and Solving Problems with Constraints, ECAI 2002
, 2002
"... We discuss the modeling and reformulation of a resource allocation problem, the assignment of Graduate Teaching Assistants to courses in the University of NebraskaLincoln Computer Science Department. ..."
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Cited by 10 (6 self)
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We discuss the modeling and reformulation of a resource allocation problem, the assignment of Graduate Teaching Assistants to courses in the University of NebraskaLincoln Computer Science Department.