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Partial Constraint Satisfaction
, 1992
"... . A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying ..."
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Cited by 443 (23 self)
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. A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed. 1 Introduction Constraint satisfaction involves finding values for problem variables subject to constraints on acceptable combinations of values. Constraint satisfaction has wide application in artificial intelligence, in areas ranging from temporal r...
Algorithms for Constraint Satisfaction Problems: A Survey
 AI MAGAZINE
, 1992
"... A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic ..."
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Cited by 399 (0 self)
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A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.
Reasoning about Qualitative Temporal Information
 Artificial Intelligence
, 1992
"... Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An intervalbased framework and a pointbased framework have been proposed for representing such temporal information. In this paper, we address ..."
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Cited by 144 (5 self)
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Representing and reasoning about incomplete and indefinite qualitative temporal information is an essential part of many artificial intelligence tasks. An intervalbased framework and a pointbased framework have been proposed for representing such temporal information. In this paper, we address two fundamental reasoning tasks that arise in applications of these frameworks: Given possibly indefinite and incomplete knowledge of the relationships between some intervals or points, (i) find a scenario that is consistent with the information provided, and (ii) find the feasible relations between all pairs of intervals or points. For the pointbased framework and a restricted version of the intervalbased framework, we give computationally efficient procedures for finding a consistent scenario and for finding the feasible relations. Our algorithms are marked improvements over the previously known algorithms. In particular, we develop an O(n 2 ) time algorithm for finding one co...
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 120 (2 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
An Optimal Coarsegrained Arc Consistency Algorithm
 Artificial Intelligence
"... The use of constraint propagation is the main feature of any constraint solver. It is thus of prime importance to manage the propagation in an efficient and effective fashion. There are two classes of propagation algorithms for general constraints: finegrained algorithms where the removal of a val ..."
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Cited by 82 (12 self)
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The use of constraint propagation is the main feature of any constraint solver. It is thus of prime importance to manage the propagation in an efficient and effective fashion. There are two classes of propagation algorithms for general constraints: finegrained algorithms where the removal of a value for a variable will be propagated to the corresponding values for other variables, and coarsegrained algorithms where the removal of a value will be propagated to the related variables. One big advantage of coarsegrained algorithms, like AC3, over finegrained algorithms, like AC4, is the ease of integration when implementing an algorithm in a constraint solver. However, finegrained algorithms usually have optimal worst case time complexity while coarsegrained algorithms don’t. For example, AC3 is an algorithm with nonoptimal worst case complexity although it is simple, efficient in practice, and widely used. In this paper we propose a coarsegrained algorithm, AC2001/3.1, that is worst case optimal and preserves as much as possible the ease of its integration into a solver (no heavy data structure to be maintained during search). Experimental results show that AC2001/3.1 is competitive with the best finegrained algorithms such as AC6. The idea behind the new algorithm can immediately be applied to obtain a path consistency algorithm that has the bestknown time and space complexity. The same idea is then extended to nonbinary constraints. Preliminary versions of this paper appeared in [BR01, ZY01].
Structured Development of Problem Solving Methods
 IEEE Transactions on Knowledge and Data Engineering
, 2001
"... Problem solving methods (PSMs) are domainindependent reasoning components, which specify patterns of behavior which can be reused across applications. While the availability of extensive PSM libraries and the emerging consensus on PSM specification languages indicate the maturity of the field, a nu ..."
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Cited by 73 (33 self)
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Problem solving methods (PSMs) are domainindependent reasoning components, which specify patterns of behavior which can be reused across applications. While the availability of extensive PSM libraries and the emerging consensus on PSM specification languages indicate the maturity of the field, a number of important research issues are still open. In particular, very little progress has been achieved on foundational and methodological issues. Existing libraries of PSMs lack a clear theoretical basis and only provide weak support for the method development process, usually in the form of informal guidelines. In this paper we will address these issues by illustrating a framework which characterizes PSMs in terms of problem commitments, problemsolving paradigms and domain assumptions. This framework provides i) a theoretical foundation for situating PSM research and individual PSMs, as well as ii) an organization which allows us to characterize method development and selection as a process of navigating through a threedimensional space (defined by the three components of our framework). Individual moves through this space are specified by means of adapters. In the paper we will illustrate these ideas in detail, with examples taken from parametric design problem solving. 1.
Using Inference to Reduce Arc Consistency Computation
 Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI’95
, 1995
"... Constraint satisfaction problems are widely used in artificial intelligence. They involve finding values for problem variables subject to constraints that specify which combinations of values are consistent. Knowledge about properties of the constraints can permit inferences that reduce the co ..."
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Cited by 66 (12 self)
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Constraint satisfaction problems are widely used in artificial intelligence. They involve finding values for problem variables subject to constraints that specify which combinations of values are consistent. Knowledge about properties of the constraints can permit inferences that reduce the cost of consistency checking. In particular, such inferences can be used to reduce the number of constraint checks required in establishing arc consistency, a fundamental constraintbased reasoning technique. A general ACInference schema is presented and various forms of inference discussed. A specific algorithm, AC7, is presented, which takes advantage of a simple property common to all binary constraints to eliminate constraint checks that other arc consistency algorithms perform. The effectiveness of this approach is demonstrated analytically, and experimentally on realworld problems.
Dynamic Variable Ordering In CSPs
, 1995
"... . We investigate the dynamic variable ordering (DVO) technique commonly used in conjunction with treesearch algorithms for solving constraint satisfaction problems. We first provide an implementation methodology for adding DVO to an arbitrary treesearch algorithm. Our methodology is applicable to ..."
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Cited by 60 (0 self)
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. We investigate the dynamic variable ordering (DVO) technique commonly used in conjunction with treesearch algorithms for solving constraint satisfaction problems. We first provide an implementation methodology for adding DVO to an arbitrary treesearch algorithm. Our methodology is applicable to a wide range of algorithms including those that maintain complicated information about the search history, like backmarking. We then investigate the popular reordering heuristic of next instantiating the variable with the minimum remaining values (MRV). We prove some interesting theorems about the MRV heuristic which demonstrate that if one wants to use the MRV heuristic one may as well use it with forward checking. Finally, we investigate the empirical performance of 12 different algorithms with and without DVO. Our experiments and theoretical results demonstrate that forward checking equipped with dynamic variable ordering is a very good algorithm for solving CSPs. 1 Introduction Despite ...
Using Constraint Metaknowledge to Reduce Arc Consistency Computation
 Artificial Intelligence
, 1999
"... Constraint satisfaction problems are widely used in articial intelligence. They involve nding values for problem variables subject to constraints that specify which combinations of values are consistent. Knowledge about properties of the constraints can permit inferences that reduce the cost of cons ..."
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Cited by 57 (8 self)
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Constraint satisfaction problems are widely used in articial intelligence. They involve nding values for problem variables subject to constraints that specify which combinations of values are consistent. Knowledge about properties of the constraints can permit inferences that reduce the cost of consistency checking. In particular, such inferences can be used to reduce the number of constraint checks required in establishing arc consistency, a fundamental constraintbased reasoning technique. A general ACInference algorithm schema is presented and various forms of inference discussed. A specific algorithm, AC7, is presented, which takes advantage of a simple property common to all binary constraints to eliminate constraint checks that other arc consistency algorithms perform. The effectiveness of this approach is demonstrated analytically, and experimentally.
Constraint propagation
 Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 56 (4 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent