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Contradicting Conventional Wisdom in Constraint Satisfaction
, 1994
"... . Constraint satisfaction problems have wide application in artificial intelligence. They involve finding values for problem variables where the values must be consistent in that they satisfy restrictions on which combinations of values are allowed. Two standard techniques used in solving such p ..."
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Cited by 206 (12 self)
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. Constraint satisfaction problems have wide application in artificial intelligence. They involve finding values for problem variables where the values must be consistent in that they satisfy restrictions on which combinations of values are allowed. Two standard techniques used in solving such problems are backtrack search and consistency inference. Conventional wisdom in the constraint satisfaction community suggests: 1) using consistency inference as preprocessing before search to prune values from consideration reduces subsequent search effort and 2) using consistency inference during search to prune values from consideration is best done at the limited level embodied in the forward checking algorithm. We present evidence contradicting both pieces of conventional wisdom, and suggesting renewed consideration of an approach which fully maintains arc consistency during backtrack search. 1 Introduction Constraint satisfaction problems (CSPs) involve finding values for prob...
Nogood Recording for Static and Dynamic Constraint Satisfaction Problems
 International Journal of Artificial Intelligence Tools
, 1993
"... Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, fo ..."
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Cited by 111 (5 self)
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Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The problem we consider here is the solution maintenance problem in such a dynamic CSP (DCSP). We propose a new class of constraint recording algorithms called Nogood Recording that may be used for solving both static and dynamic CSPs. It offers an interesting compromise, polynomially bounded in space, between an ATMSlike approach and the usual static constraint satisfaction algorithms. 1 Introduction The constraint satisfaction problem (CSP) model is widely used to represent and solve various AI related problems and provides fundamental tools in areas such as truth...
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 57 (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 ...
Variable and value ordering heuristics for the job shop scheduling constraint satisfaction problem
 Artificial Intelligence
, 1996
"... Practical Constraint Satisfaction Problems (CSPs) such as design of integrated circuits or scheduling generally entail large search spaces with hundreds or even thousands of variables, each with hundreds or thousands of possible values. Often, only a very tiny fraction of all these possible assignme ..."
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Cited by 52 (1 self)
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Practical Constraint Satisfaction Problems (CSPs) such as design of integrated circuits or scheduling generally entail large search spaces with hundreds or even thousands of variables, each with hundreds or thousands of possible values. Often, only a very tiny fraction of all these possible assignments participates in a satisfactory solution. This article discusses techniques that aim at reducing the effective size of the search space to be explored in order to find a satisfactory solution by judiciously selecting the order in which variables are instantiated and the sequence in which possible values are tried for each variable. In the CSP literature, these techniques are commonly referred to as variable and value ordering heuristics. Our investigation is conducted in the job shop scheduling domain. We show that, in contrast with problems studied earlier in the CSP literature, generic variable and value heuristics do not perform well in this domain. This is attributed to the difficulty of these heuristics to properly account for the tightness of constraints and/or the connectivity of the constraint graphs induced by job shop scheduling CSPs. A new probabilistic framework is introduced that better captures these key aspects of the job shop scheduling search space. Empirical results show that variable and value ordering heuristics
The Complexity Of Maximal Constraint Languages
, 2001
"... Many combinatorial search problems can be expressed as "constraint satisfaction problems" using an appropriate "constraint language", that is, a set of relations over some fixed finite set of values. It is wellknown that there is a tradeoff between the expressive power of a constraint language and ..."
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Cited by 35 (8 self)
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Many combinatorial search problems can be expressed as "constraint satisfaction problems" using an appropriate "constraint language", that is, a set of relations over some fixed finite set of values. It is wellknown that there is a tradeoff between the expressive power of a constraint language and the complexity of the problems it can express. In the present paper we systematically study the complexity of all maximal constraint languages, that is, languages whose expressive power is just weaker than that of the language of all constraints. Using the algebraic invariance properties of constraints, we exhibit a strong necessary condition for tractability of such a constraint language. Moreover, we show that, at least for small sets of values, this condition is also sufficient.
Intelligent Backtracking Techniques for Job Shop Scheduling
 In Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning
, 1992
"... This paper studies a version of the job shop scheduling problem in which some operations have to be scheduled within nonrelaxable time windows (i.e. earliest/latest possible start time windows). This problem is a wellknown NPcomplete Constraint Satisfaction Problem (CSP). A popular method for solv ..."
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Cited by 33 (4 self)
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This paper studies a version of the job shop scheduling problem in which some operations have to be scheduled within nonrelaxable time windows (i.e. earliest/latest possible start time windows). This problem is a wellknown NPcomplete Constraint Satisfaction Problem (CSP). A popular method for solving these types of problems consists in using depthfirst backtrack search. Our earlier work focused on developing efficient consistency enforcing techniques and efficient variable /value ordering heuristics to improve the efficiency of this procedure. In this paper, we combine these techniques with new lookback schemes that help the search procedure recover from socalled deadend search states (i.e. partial solutions that cannot be completed without violating some constraints). More specifically, we successively describe three intelligent backtracking schemes: Dynamic Consistency Enforcement dynamically enforces higher levels of consistency in selected critical subproblems, Learning From Fa...
Multiway Spatial Joins
 ACM Transactions on Database Systems (TODS
, 2001
"... Due to the evolution of Geographical Information Systems, large collections of spatial data having various thematic contents are currently available. As a result, the interest of users is not limited to simple spatial selections and joins, but complex query types that implicate numerous spatial inpu ..."
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Cited by 32 (8 self)
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Due to the evolution of Geographical Information Systems, large collections of spatial data having various thematic contents are currently available. As a result, the interest of users is not limited to simple spatial selections and joins, but complex query types that implicate numerous spatial inputs become more common. Although several algorithms have been proposed for computing the result of pairwise spatial joins, limited work exists on processing and optimization of multiway spatial joins. In this article, we review pairwise spatial join algorithms and show how they can be combined for multiple inputs. In addition, we explore the application of synchronous traversal (ST), a methodology that processes synchronously all inputs without producing intermediate results. Then, we integrate the two approaches in an engine that includes ST and pairwise algorithms, using dynamic programming to determine the optimal execution plan. The results show that, in most cases, multiway spatial joins are best processed by combining ST with pairwise methods. Finally, we study the optimization of very large queries by employing randomized search algorithms.
Is there any Need for DomainDependent Control Information?
 In Proceedings of the Ninth National Conference on Artificial Intelligence
, 1991
"... No. 1 Introduction The split between baselevel and metalevel knowledge has long been recognized by the declarative community. Roughly speaking, baselevel knowledge has to do with information about some particular domain, while metalevel knowledge has to do with knowledge about that information. ..."
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Cited by 17 (2 self)
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No. 1 Introduction The split between baselevel and metalevel knowledge has long been recognized by the declarative community. Roughly speaking, baselevel knowledge has to do with information about some particular domain, while metalevel knowledge has to do with knowledge about that information. A typical baselevel fact might be, "Iraq invaded Kuwait," while a typical metalevel fact might be, "To show that a country c is aggressive, first try to find another country that has been invaded by c." Baselevel information is of necessity domaindependent, since the facts presented will involve the particular domain about which the system is expected to reason. Metalevel information, however, can be either domaindependent (as in the example of the previous paragraph and as typically described in [Silver,1986]), or domainindependent. Typical domainindependent metalevel rules are the cheapestfirst heuristic or the results found in Smith's work on control of inference [Smith,1986, Smi...
Approximate processing of multiway spatial joins in very large databases
 Proceedings of 8th EDBT Conference
, 2002
"... Abstract. Existing work on multiway spatial joins focuses on the retrieval of all exact solutions with no time limit for query processing. Depending on the query and data properties, however, exhaustive processing of multiway spatial joins can be prohibitively expensive due to the exponential nature ..."
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Cited by 6 (0 self)
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Abstract. Existing work on multiway spatial joins focuses on the retrieval of all exact solutions with no time limit for query processing. Depending on the query and data properties, however, exhaustive processing of multiway spatial joins can be prohibitively expensive due to the exponential nature of the problem. Furthermore, if there do not exist any exact solutions, the result will be empty even though there may exist solutions that match the query very closely. These shortcomings motivate the current work, which aims at the retrieval of the best possible (exact or approximate) solutions within a time threshold, since fast retrieval of approximate matches is the only way to deal with the ever increasing amounts of multimedia information in several real time systems. We propose various techniques that combine local and evolutionary search with underlying indexes to prune the search space. In addition to their usefulness as standalone methods for approximate query processing, the techniques can be combined with systematic search to enhance performance when the goal is retrieval of the best solutions. 1.
Constraint Satisfaction  Algorithms and Complexity Analysis
 Information Processing Letters
, 1994
"... The constraint satisfaction problem (CSP) comprises n variables with associated finite domains (with a maximal cardinality d ), and some combinations of value assignments ("constraints") to the variables; then, in order to get the globally consistent solution, we need to compute the set of all ntup ..."
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Cited by 5 (0 self)
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The constraint satisfaction problem (CSP) comprises n variables with associated finite domains (with a maximal cardinality d ), and some combinations of value assignments ("constraints") to the variables; then, in order to get the globally consistent solution, we need to compute the set of all ntuples consistent with the given constraints. There are a lot of papers which exploit specific constraint network structures; others focus on local constraint propagation. However, finally, the global solution is wanted, and in this regard, I would like to introduce here a general framework which really yields this globally consistent solution. It is wellknown that local consistency does not imply global consistency. Anyway, to start directly with a higherlevel mechanism may not be a bad idea. The algorithms presented here may get consulted when nothing can be exploited regarding network topology or other features. Remark This report may supersede #14/90. The current issue (#17/94) is a slig...