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Constraint Networks
, 1992
"... Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expression ..."
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Cited by 948 (42 self)
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Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expressions. These have been successfully applied to diverse tasks such as design, diagnosis, truth maintenance, scheduling, spatiotemporal reasoning, logic programming and user interface. Constraint networks are graphical representations used to guide strategies for solving constraint satisfaction problems (CSPs).
Bucket Elimination: A Unifying Framework for Reasoning
"... Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination ..."
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Cited by 278 (62 self)
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Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination for solving linear equalities and inequalities, and dynamic programming for combinatorial optimization, can all be accommodated within the bucket elimination framework. Many probabilistic inference tasks can likewise be expressed as bucketelimination algorithms. These include: belief updating, finding the most probable explanation, and expected utility maximization. These algorithms share the same performance guarantees; all are time and space exponential in the inducedwidth of the problem's interaction graph. While elimination strategies have extensive demands on memory, a contrasting class of algorithms called "conditioning search" require only linear space. Algorithms in this class split a problem into subproblems by instantiating a subset of variables, called a conditioning set, or a cutset. Typical examples of conditioning search algorithms are: backtracking (in constraint satisfaction), and branch and bound (for combinatorial optimization). The paper presents the bucketelimination framework as a unifying theme across probabilistic and deterministic reasoning tasks and show how conditioning search can be augmented to systematically trade space for time.
Directional Resolution: The DavisPutnam Procedure, Revisited
 IN PROCEEDINGS OF KR94
, 1994
"... The paper presents an algorithm called directional resolution, a variation on the original DavisPutnam algorithm, and analyzes its worstcase behavior as a function of the topological structure of propositional theories. The concepts of induced width and diversity are shown to play a key role in ..."
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Cited by 101 (22 self)
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The paper presents an algorithm called directional resolution, a variation on the original DavisPutnam algorithm, and analyzes its worstcase behavior as a function of the topological structure of propositional theories. The concepts of induced width and diversity are shown to play a key role in bounding the complexity of the procedure. The importance of our analysis lies in highlighting structurebased tractable classes of satisfiability and in providing theoretical guarantees on the time and space complexity of the algorithm. Contrary to previous assessments, we show that for many theories directional resolution could be an effective procedure. Our empirical tests confirm theoretical prediction, showing that on problems with a special structure, namely ktree embeddings (e.g. chains, (k,m)trees), directional resolution greatly outperforms one of the most effective satisfiability algorithms known to date, the popular DavisPutnam procedure. Furthermore, combining a bounded...
On the Feasibility of Distributed Constraint Satisfaction
, 1991
"... This paper characterizes connectionisttype architectures that allow a distributed solution for classes of constraintsatisfaction problems. The main issue addressed is whether there exists a uniform model of computation (where all nodes are indistinguishable) that guarantees convergence to a ..."
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Cited by 69 (12 self)
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This paper characterizes connectionisttype architectures that allow a distributed solution for classes of constraintsatisfaction problems. The main issue addressed is whether there exists a uniform model of computation (where all nodes are indistinguishable) that guarantees convergence to a solution from every initial state of the system, whenever such a solution exists. We show that even for relatively simple constraint networks, such as rings, there is no general solution using a completely uniform, asynchronous, model. However, some restricted topologies like trees can accommodate the uniform, asynchronous, model and a protocol demonstrating this fact is presented. An almostuniform, asynchronous, networkconsistency protocol is also presented. We show that the algorithms are guaranteed to be selfstabilizing, which makes them suitable for dynamic or errorprone environments. 1 Introduction Consider the distributed version of the graph coloring problem, where ea...
Random constraint satisfaction: Flaws and structure
 Constraints
, 2001
"... 4, and Toby Walsh 5 ..."
Local and global relational consistency
 THEORETICAL COMPUTER SCIENCE
, 1997
"... Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relationbased, in contrast with the previous definition of local consiste ..."
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Cited by 61 (15 self)
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Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relationbased, in contrast with the previous definition of local consistency, which we characterize as variablebased. We show the conceptual power of the new definition by showing how it unifies known elimination operators such as resolution in theorem proving, joins in relational databases, and variable elimination for solving linear inequalities. Algorithms for enforcing various levels of relational consistency are introduced and analyzed. We also show the usefulness of the new definition in characterizing relationships between properties of constraint networks and the level of local consistency needed to ensure global consistency.
Topological Parameters for timespace tradeoff
 Artificial Intelligence
, 1996
"... In this paper we propose a family of algorithms combining treeclustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks. By analyzing the problem structure it will be p ..."
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Cited by 58 (12 self)
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In this paper we propose a family of algorithms combining treeclustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks. By analyzing the problem structure it will be possible to select from a spectrum the algorithm that best meets a given timespace specification. 1 INTRODUCTION Topologybased algorithms for constraint satisfaction and probabilistic reasoning fall into two distinct classes. One class is centered on treeclustering, the other on cyclecutset decomposition. Treeclustering involves transforming the original problem into a treelike problem that can then be solved by a specialized treesolving algorithm [ Mackworth and Freuder, 1985; Pearl, 1986 ] . The treeclustering algorithm is time and space exponential in the induced width (also called tree width) of the problem's graph. The transforming algorithm identifies subproblems that together ...
On the Minimality and Global Consistency of RowConvex Constraint Networks
, 1992
"... Constraint networks have beenshown to be useful in formulating such diverse problems as scene labeling, natural language parsing, and temporal reasoning. Given a constraint network, we often wish to (i) nd a solution that satis es the constraints and (ii) nd the corresponding minimal network where t ..."
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Cited by 46 (3 self)
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Constraint networks have beenshown to be useful in formulating such diverse problems as scene labeling, natural language parsing, and temporal reasoning. Given a constraint network, we often wish to (i) nd a solution that satis es the constraints and (ii) nd the corresponding minimal network where the constraints are as explicit as possible. Both tasks are known to be NPcomplete in the general case. Task (i) is usually solved using a backtracking algorithm, and task (ii) is often solved only approximately by enforcing various levels of local consistency. In this paper, we identify a property of binary constraints called row convexity and show its usefulness in deciding when a form of local consistency called path consistency is sufficient to guarantee that a network is both minimal and globally consistent. Globally consistent networks have the property that a solution can be found without backtracking. We show that one can test for the row convexity property e ciently and we show, by examining
Backjumpbased Backtracking for Constraint Satisfaction Problems
 Artificial Intelligence
, 2002
"... The performance of backtracking algorithms for solving finitedomain constraint satisfaction problems can be improved substantially by lookback and lookahead methods. Lookback techniques extract information by analyzing failing search paths that are terminated by deadends. Lookahead techniques ..."
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Cited by 37 (2 self)
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The performance of backtracking algorithms for solving finitedomain constraint satisfaction problems can be improved substantially by lookback and lookahead methods. Lookback techniques extract information by analyzing failing search paths that are terminated by deadends. Lookahead techniques use constraint propagation algorithms to avoid such deadends altogether. This survey describes a number of lookback variants including backjumping and constraint recording which recognize and avoid some unnecessary explorations of the search space. The last portion of the paper gives an overview of lookahead methods such as forward checking and dynamic variable ordering, and discusses their combination with backjumping.
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...