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43
Hybrid Algorithms for the Constraint Satisfaction Problem
 Computational Intelligence
, 1993
"... problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflictdirected backjumping ..."
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Cited by 347 (7 self)
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problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflictdirected backjumping
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 137 (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...
The Constrainedness of Search
 In Proceedings of AAAI96
, 1999
"... We propose a definition of `constrainedness' that unifies two of the most common but informal uses of the term. These are that branching heuristics in search algorithms often try to make the most "constrained" choice, and that hard search problems tend to be "critically constrained". Our definition ..."
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Cited by 116 (26 self)
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We propose a definition of `constrainedness' that unifies two of the most common but informal uses of the term. These are that branching heuristics in search algorithms often try to make the most "constrained" choice, and that hard search problems tend to be "critically constrained". Our definition of constrainedness generalizes a number of parameters used to study phase transition behaviour in a wide variety of problem domains. As well as predicting the location of phase transitions in solubility, constrainedness provides insight into why problems at phase transitions tend to be hard to solve. Such problems are on a constrainedness "knifeedge", and we must search deep into the problem before they look more or less soluble. Heuristics that try to get off this knifeedge as quickly as possible by, for example, minimizing the constrainedness are often very effective. We show that heuristics from a wide variety of problem domains can be seen as minimizing the constrainedness (or proxies ...
Fuzzy Constraint Satisfaction
 In Proc. 3rd IEEE International Conference on Fuzzy Systems
, 1994
"... In this paper the issue of soft constraint satisfaction is discussed from a fuzzy set theoretical point of view. A fuzzy constraint is considered as a fuzzy relation. Different possible definitions for the degree of joint satisfaction of a set of fuzzy constraints are given, covering specific other ..."
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Cited by 95 (0 self)
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In this paper the issue of soft constraint satisfaction is discussed from a fuzzy set theoretical point of view. A fuzzy constraint is considered as a fuzzy relation. Different possible definitions for the degree of joint satisfaction of a set of fuzzy constraints are given, covering specific other soft constraint satisfaction problem (CSP) types such a partial and hierarchical CSP. It is shown that the classical CSP solving heuristics based on variable and value evaluations can be generalised and used to guide the solution construction process for solving fuzzy CSPs, and that the heuristic search can be replaced by branchandbound search. The solution process is illustrated with an example from the CSP literature. Finally, research issues are discussed. 1. Introduction In the recent years there has been a growing interest in soft constraint satisfaction. In general, in a soft CSP not all the given constraints need to be satisfied  either because all of them cannot be met, theoret...
Complexity and Algorithms for Reasoning About Time: A GraphTheoretic Approach
, 1992
"... Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence ..."
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Cited by 86 (11 self)
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Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics. The satisfiability, minimal labeling, all solutions and all realizations problems are considered for temporal (interval) data. Several versions are investigated by restricting the possible interval relationships yielding different complexity results. We show that even when the temporal data comprises of subsets of relations based on intersection and precedence only, the satisfiability question is NPcomplete. On the positive side, we give efficient algorithms for several restrictions of the problem. In the process, the interval graph sandwich problem is introduced, and is shown to be NPcomplete. This problem is als...
An Empirical Study of Dynamic Variable Ordering Heuristics for the Constraint Satisfaction Problem
 In Proceedings of CP96
, 1996
"... . The constraint satisfaction community has developed a number of heuristics for variable ordering during backtracking search. For example, in conjunction with algorithms which check forwards, the FailFirst (FF) and Brelaz (Bz) heuristics are cheap to evaluate and are generally considered to be ver ..."
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Cited by 69 (15 self)
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. The constraint satisfaction community has developed a number of heuristics for variable ordering during backtracking search. For example, in conjunction with algorithms which check forwards, the FailFirst (FF) and Brelaz (Bz) heuristics are cheap to evaluate and are generally considered to be very effective. Recent work to understand phase transitions in NPcomplete problem classes enables us to compare such heuristics over a large range of different kinds of problems. Furthermore, we are now able to start to understand the reasons for the success, and therefore also the failure, of heuristics, and to introduce new heuristics which achieve the successes and avoid the failures. In this paper, we present a comparison of the Bz and FF heuristics in forward checking algorithms applied to randomlygenerated binary CSP's. We also introduce new and very general heuristics and present an extensive study of these. These new heuristics are usually as good as or better than Bz and FF, and we id...
Experimental evaluation of preprocessing techniques in constraint satisfaction problems
 In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence
, 1989
"... This paper presents an evaluation of two orthogonal schemes for improving the efficiency of solving constraint satisfaction problems (CSPs). The first scheme involves a class of preprocessing techniques designed to make the representation of the CSP more explicit, including directionalarcconsisten ..."
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Cited by 54 (10 self)
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This paper presents an evaluation of two orthogonal schemes for improving the efficiency of solving constraint satisfaction problems (CSPs). The first scheme involves a class of preprocessing techniques designed to make the representation of the CSP more explicit, including directionalarcconsistency, directionalpathconsistency and adaptiveconsistency. The second scheme aims at improving the order in which variables are chosen for evaluation during the search. In the first part of the experiment we tested the performance of backtracking (and its common enhancementbackjumping) with and without each of the preprocessings techniques above. The results show that directional arcconsistency, a scheme which embodies the simplest form of constraint recording, outperforms all other preprocessing techniques. The results of the second part of the experiment suggest that the best variable ordering is achieved by the fixed maxcardinality search order. 1.
The Combinatorics of Object Recognition in Cluttered Environments using Constrained Search
, 1988
"... The problem of recognizing rigid objects from noisy sensory data has been successfully attacked in previous work by using a constrained search approach. Empirical investigations have shown the method to be very effective when recognizing and localizing isolated objects, but less effective when deali ..."
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Cited by 53 (2 self)
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The problem of recognizing rigid objects from noisy sensory data has been successfully attacked in previous work by using a constrained search approach. Empirical investigations have shown the method to be very effective when recognizing and localizing isolated objects, but less effective when dealing with occluded objects where much of the sensory data arises from objects other than the one of interest. When clustering techniques such as the Hough transform are used to isolate likely subspaces of the search space, empiricial performance in cluttered scenes improves considerably. In this note, we establish formal bounds on the combinatories of this approach. Under some simple assumptions, we show that the expected complexity of recognizing isolated objects is quadratic in the number of model and sensory fragments, but that the expected complexity of recognizing objects in cluttered environments is exponential in the size of the correct interpretation. We also provide formal bounds on the efficacy of using the Hough transform to preselect likely subspaces, showing that problem remains exponential, but that in practical terms, the size of the problem is significantly decreased.
Trying Harder to Fail First
 In: Thirteenth European Conference on Artificial Intelligence (ECAI 98
, 1997
"... Variable ordering heuristics can have a profound effect on the performance of backtracking search algorithms for constraint satisfaction problems. The smallestremainingdomain heuristic is a commonlyused dynamic variable ordering heuristic, used in conjunction with algorithms such as forward checki ..."
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Cited by 49 (1 self)
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Variable ordering heuristics can have a profound effect on the performance of backtracking search algorithms for constraint satisfaction problems. The smallestremainingdomain heuristic is a commonlyused dynamic variable ordering heuristic, used in conjunction with algorithms such as forward checking which look ahead at the effects of each variable instantiation on those variables not yet instantiated. This heuristic has been explained as an implementation of the failfirst principle, stated by Haralick and Elliott [7], i.e. that the next variable selected should be the one which is most likely to result in an immediate failure. We calculate the probability that a variable will fail when using the forward checking algorithm to solve a class of binary CSPs. We derive a series of heuristics, starting with smallestremainingdomain, based on increasingly accurate estimates of this probability, and predict that if the failfirst principle is sound, the more accurate the estimate the better...
The Constrainedness of Arc Consistency
 in Proceedings of CP97
, 1997
"... . We show that the same methodology used to study phase transition behaviour in NPcomplete problems works with a polynomial problem class: establishing arc consistency. A general measure of the constrainedness of an ensemble of problems, used to locate phase transitions in random NPcomplete proble ..."
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Cited by 45 (9 self)
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. We show that the same methodology used to study phase transition behaviour in NPcomplete problems works with a polynomial problem class: establishing arc consistency. A general measure of the constrainedness of an ensemble of problems, used to locate phase transitions in random NPcomplete problems, predicts the location of a phase transition in establishing arc consistency. A complexity peak for the AC3 algorithm is associated with this transition. Finite size scaling models both the scaling of this transition and the computational cost. On problems at the phase transition, this model of computational cost agrees with the theoretical worst case. As with NPcomplete problems, constrainedness  and proxies for it which are cheaper to compute  can be used as a heuristic for reducing the number of checks needed to establish arc consistency in AC3. 1 Introduction Following [4] there has been considerable research into phase transition behaviour in NPcomplete problems. Problems from...