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36
Adaptive Constraint Satisfaction
 WORKSHOP OF THE UK PLANNING AND SCHEDULING
, 1996
"... Many different approaches have been applied to constraint satisfaction. These range from complete backtracking algorithms to sophisticated distributed configurations. However, most research effort in the field of constraint satisfaction algorithms has concentrated on the use of a single algorithm fo ..."
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Cited by 811 (43 self)
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Many different approaches have been applied to constraint satisfaction. These range from complete backtracking algorithms to sophisticated distributed configurations. However, most research effort in the field of constraint satisfaction algorithms has concentrated on the use of a single algorithm for solving all problems. At the same time, a consensus appears to have developed to the effect that it is unlikely that any single algorithm is always the best choice for all classes of problem. In this paper we argue that an adaptive approach should play an important part in constraint satisfaction. This approach relaxes the commitment to using a single algorithm once search commences. As a result, we claim that it is possible to undertake a more focused approach to problem solving, allowing for the correction of bad algorithm choices and for capitalising on opportunities for gain by dynamically changing to more suitable candidates.
A Theoretical Evaluation of Selected Backtracking Algorithms
 Artificial Intelligence
, 1997
"... In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a di erent, purely theoretical approach, which is based on charact ..."
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Cited by 115 (3 self)
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In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a di erent, purely theoretical approach, which is based on characterizations of the sets of search treenodes visited by the backtracking algorithms. A notion of inconsistency between instantiations and variables is introduced, and is shown to be a useful tool for characterizing such wellknown concepts as backtrack, backjump, and domain annihilation. The characterizations enable us to: (a) prove the correctness of the algorithms, and (b) partially order the algorithms according to two standard performance measures: the number of nodes visited, and the number of consistency checks performed. Among other results, we prove the correctness of Backjumping and Con ictDirected Backjumping, and show that Forward Checking never visits more nodes than Backjumping. Our approach leads us also to propose a modi cation to two hybrid backtracking algorithms, Backmarking with Backjumping (BMJ) and Backmarking with Con ictDirected Backjumping (BMCBJ), so that they always perform fewer consistency checks than the original algorithms. 1
A Polynomial Time Algorithm for the NQueens Problem
, 1990
"... this paper we present a new, probabilistic local search algorithm which is based on a gradientbased heuristic. This efficient algorithm is capable of finding a solution for extremely large size nqueens problems. We give the execution statistics for this algorithm with n up to 500,000. Keywords: Ar ..."
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Cited by 32 (4 self)
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this paper we present a new, probabilistic local search algorithm which is based on a gradientbased heuristic. This efficient algorithm is capable of finding a solution for extremely large size nqueens problems. We give the execution statistics for this algorithm with n up to 500,000. Keywords: Artificial intelligence (AI), combinatorial search, gradientbased heuristic, local search, the nqueens problem, nonbacktracking search, fast search algorithm. 1
Dual Modelling of Permutation and Injection Problems
 Journal of Artificial Intelligence Research
, 2004
"... When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many ..."
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Cited by 30 (9 self)
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When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many values as variables, and each variable takes an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable represents one of the primal values, whilst each dual value represents one of the primal variables. Alternatively, by means of channelling constraints to link the primal and dual variables, we can have a combined model with both sets of variables. In this paper, we perform an extensive theoretical and empirical study of such primal, dual and combined models for two classes of problems: permutation problems and injection problems. Our results show that it often be advantageous to use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general...
Interchangeability Supports Abstraction and Reformulation for Constraint Satisfaction
 In Proceedings of Symposium on Abstraction, Reformulation and Approximation (SARA'95
, 1995
"... Abstraction and reformulation are fundamental, powerful ideas in artificial intelligence, but they have not had a great deal of application in the area of constraint satisfaction. The obvious way to implement abstraction in a constraint satisfaction context is to simplify the problem by removing con ..."
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Cited by 29 (1 self)
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Abstraction and reformulation are fundamental, powerful ideas in artificial intelligence, but they have not had a great deal of application in the area of constraint satisfaction. The obvious way to implement abstraction in a constraint satisfaction context is to simplify the problem by removing constraints, and then use the solutions to the simplified problem to guide the search for a solution to the original problem. In a sense, local search, hill climbing methods use this approach, while giving up completeness guarantees. The problem for a complete method is that a simplified problem may be trivial (recent work on locating hard problems suggests that hard problems may cluster on narrow ridges in problem space). Thus there may be too many solutions to the simplified problem to be useful. The Cartesian product representation and interchangeability techniques provide ways of working with compact representations of large sets of solutions.
Binary vs. nonbinary constraints
 Artificial Intelligence
, 2002
"... Fellowship program. 1 There are two well known transformations from nonbinary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the dual transformation and the hidden (variable) transformation. We perform a detailed formal comparison of the ..."
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Cited by 23 (2 self)
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Fellowship program. 1 There are two well known transformations from nonbinary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the dual transformation and the hidden (variable) transformation. We perform a detailed formal comparison of these two transformations. Our comparison focuses on two backtracking algorithms that maintain a local consistency property at each node in their search tree: the forward checking and maintaining arc consistency algorithms. We first compare local consistency techniques such as arc consistency in terms of their inferential power when they are applied to the original (nonbinary) formulation and to each of its binary transformations. For example, we prove that enforcing arc consistency on the original formulation is equivalent to enforcing it on the hidden transformation. We then extend these results to the two backtracking algorithms. We are able to give either a theoretical bound on how much one formulation is better than another, or examples that show such a bound does not exist. For example, we prove that the performance of the forward checking algorithm applied to the hidden transformation of a problem is within a polynomial bound of the performance of the same algorithm applied to the dual transformation of the problem. Our results can be used to help decide if applying one of these transformations to all (or part) of a constraint satisfaction model would be beneficial. 2 1
Constraint Programming Lessons Learned from Crossword Puzzles
 In Proceedings of the 14th Canadian Conference on Artificial Intelligence
, 2001
"... Constraint programming is a methodology for solving di cult combinatorial problems. In the methodology, one makes three design decisions: the constraint model, the search algorithm for solving the model, and the heuristic for guiding the search. Previous work has shown that the three design dec ..."
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Cited by 20 (1 self)
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Constraint programming is a methodology for solving di cult combinatorial problems. In the methodology, one makes three design decisions: the constraint model, the search algorithm for solving the model, and the heuristic for guiding the search. Previous work has shown that the three design decisions can greatly inuence the eciency of a constraint programming approach. However, what has not been explicitly addressed in previous work is to what level, if any, the three design decisions can be made independently. In this paper we use crossword puzzle generation as a case study to examine this question. We draw the following general lessons from our study. First, that the three design decisionsmodel, algorithm, and heuristicare mutually dependent. As a consequence, in order to solve a problem using constraint programming most eciently, one must exhaustively explore the space of possible models, algorithms, and heuristics. Second, that if we do assume some form of independence when making our decisions, the resulting decisions can be suboptimal by orders of magnitude.
Using CBR to select solution strategies in constraint programming
 In ICCBR
, 2005
"... Abstract. Constraint programming is a powerful paradigm that offers many different strategies for solving problems. Choosing a good strategy is difficult; choosing a poor strategy wastes resources and may result in a problem going unsolved. We show how CaseBased Reasoning can be used to select good ..."
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Cited by 19 (0 self)
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Abstract. Constraint programming is a powerful paradigm that offers many different strategies for solving problems. Choosing a good strategy is difficult; choosing a poor strategy wastes resources and may result in a problem going unsolved. We show how CaseBased Reasoning can be used to select good strategies. We design experiments which demonstrate that, on two problems with quite different characteristics, CBR can outperform four other strategy selection techniques. 1
Reanalysis and Limited Repair Parsing: Leaping off the Garden Path
, 1998
"... This chapter develops a theory of reanalysis called limited repair parsing. Repair parsers deal with the problem of local ambiguity in part by modifying previously built structure when the chosen structure later proves to be inconsistent. This modification of existing structure distinguishes repair ..."
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Cited by 8 (1 self)
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This chapter develops a theory of reanalysis called limited repair parsing. Repair parsers deal with the problem of local ambiguity in part by modifying previously built structure when the chosen structure later proves to be inconsistent. This modification of existing structure distinguishes repair parsing from parallel or multipath parsing, leastcommitment parsing, backtracking, or reparsing strategies. Parsers with a limited capability for repair are psycholinguistically important because they can potentially explain the contrasts between difficult garden path structures (when repair fails) and unproblematic local ambiguities (when repair is successful or easy). Although the idea of repair has been implicit in some psycholinguistic work (and emerged explicitly in the diagnosis model of Fodor & Inoue, 1994, and the NLSoar model of Lewis, 1993), there has been no clear formulation of the general class of repair parsers. This chapter makes a first step toward such a formulation, show...
Capturing Constraint Programming Experience: A CaseBased Approach
, 2002
"... The spread of constraint technology is inhibited by the lack of experienced constraint programmers. We present here a proposal for a tool that uses CaseBased Reasoning to store, retrieve and reuse constraint programming experience. We report our initial design ideas, and we sketch how the tool will ..."
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Cited by 8 (4 self)
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The spread of constraint technology is inhibited by the lack of experienced constraint programmers. We present here a proposal for a tool that uses CaseBased Reasoning to store, retrieve and reuse constraint programming experience. We report our initial design ideas, and we sketch how the tool will operate in the domain of logic puzzles.