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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
Analysis of Distributed ArcConsistency Algorithms
, 1997
"... Consistency techniques can significantly reduce the search space of constraint satisfaction problems (CSP). In particular, arcconsistency algorithms, such as AC3 [7], AC4 [8] and AC6 [2], have been designed. In [9], we presented DisAC4, a coarsegrained parallel algorithm designed for distribut ..."
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Cited by 44 (0 self)
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Consistency techniques can significantly reduce the search space of constraint satisfaction problems (CSP). In particular, arcconsistency algorithms, such as AC3 [7], AC4 [8] and AC6 [2], have been designed. In [9], we presented DisAC4, a coarsegrained parallel algorithm designed for distributed memory computer using message passing, which is a distributed version of AC4. We extend here this result. We design DisAC3 and DisAC6. The communication scheme is also extended to allow communication during the propagation step of the consistency algorithms. All these algorithms were systematically experimented. An analysis of the different experiments shows that, as in the sequential case, DisAC6 provides the best performance and that DisAC3 outperforms DisAC4 on most tests. All the distributed algorithms shows a linear speedup. This lead to the conclusion that DisAC6 is a good candidate for distributed arcconsistency.
Mixing Constraints and Objects: a Case Study in Automatic Harmonization
"... We propose an extension of Smalltalk with finitedomain constraint satisfaction mechanisms. Our system, called BackTalk, allows the definition of constraints over arbitrary Smalltalk objects, and implements efficient algorithms for constraints satisfaction. We exemplify the use of BackTalk on a prob ..."
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Cited by 18 (4 self)
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We propose an extension of Smalltalk with finitedomain constraint satisfaction mechanisms. Our system, called BackTalk, allows the definition of constraints over arbitrary Smalltalk objects, and implements efficient algorithms for constraints satisfaction. We exemplify the use of BackTalk on a problem known to be complex, automatic harmonization. We outline several previous attempts to solve the problem with similar mechanisms, and stress on their inefficiencies, mainly the lack of structure of domain objects. We propose to solve the problem by a combination of constraints and objects that fully benefits from object structures. This is achieved in practice by separating the constraint satisfaction process in two steps. By comparison, our system yields excellent results, both in term of efficiency and readability. We discuss the generality of our approach to problems involving numerous and heterogeneous object structures. Keywords: constraints, finitedomain constraint satisfaction, ...
An expectedcost analysis of backtracking and nonbacktracking algorithms
 In Procceedings of the International Joint Conference on Artifical Intelligence (IJCAI
, 1991
"... Consider an infinite binary search tree in which the branches have independent random costs. Suppose that we must find an optimal (cheapest) or nearly optimal path from the root to a node at depth n. Karp and Pearl [1983] show that a boundedlookahead backtracking algorithm A2 usually finds a nearly ..."
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Cited by 9 (0 self)
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Consider an infinite binary search tree in which the branches have independent random costs. Suppose that we must find an optimal (cheapest) or nearly optimal path from the root to a node at depth n. Karp and Pearl [1983] show that a boundedlookahead backtracking algorithm A2 usually finds a nearly optimal path in linear expected time (when the costs take only the values 0 or 1). From this successful performance one might conclude that similar heuristics should be of more general use. But we find here equal success for a simpler nonbacktracking boundedlookahead algorithm, so the search model cannot support this conclusion. If, however, the search tree is generated by a branching process so that there is a possibility of nodes having no sons (or branches having prohibitive costs), then the nonbacktracking algorithm is hopeless while the backtracking algorithm still performs very well. These results suggest the general guideline that backtracking becomes attractive when there is the possibility of "deadends " or prohibitively costly outcomes.
Empirical Modeling of Genetic Algorithms
 EVOLUTIONARY COMPUTATION
, 2001
"... This paper addresses the problem of reliably setting genetic algorithm parameters for consistent labelling problems. Genetic algorithm parameters are notoriously difficult to determine. This paper proposes a robust empirical framework, based on the analysis of factorial experiments. The use of a gra ..."
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Cited by 7 (1 self)
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This paper addresses the problem of reliably setting genetic algorithm parameters for consistent labelling problems. Genetic algorithm parameters are notoriously difficult to determine. This paper proposes a robust empirical framework, based on the analysis of factorial experiments. The use of a graecolatin square permits an initial study of a wide range of parameter settings. This is followed by fully crossed factorial experiments with narrower ranges, which allow detailed analysis by logistic regression. The empirical models thus derived can be used first to determine optimal algorithm parameters, and second to shed light on interactions between the parameters and their relative importance. The initial models do not extrapolate well. However, an advantage of this approach is that the modelling process is under the control of the experimenter, and is hence very flexible. Refined models are produced, which are shown to be robust under extrapolation to up to triple the problem size.
An Examination of Probabilistic ValueOrdering Heuristics
 In Proceedings of the 12th Australian Joint Conference on Artificial Intelligence
, 1999
"... . Searching for solutions to constraint satisfaction problems (CSPs) is NPhard in general. Heuristics for variable and value ordering have proven useful in guiding the search towards more fruitful areas of the search space and hence reducing the amount of time spent searching for solutions. Sta ..."
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Cited by 4 (2 self)
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. Searching for solutions to constraint satisfaction problems (CSPs) is NPhard in general. Heuristics for variable and value ordering have proven useful in guiding the search towards more fruitful areas of the search space and hence reducing the amount of time spent searching for solutions. Static ordering methods impart an ordering in advance of the search and dynamic ordering methods use information about the state of the search to order values or variables during the search. A wellknown static value ordering heuristic guides the search by ordering values basedon an estimate of the number of solutions to the problem. This paper compares the performance of several such heuristics and shows that they do not give a significant improvement to a random ordering for hard CSPs. We give a dynamic ordering heuristic which decomposesthe CSP into spanning trees and uses Bayesian networks to compute probabilistic approximations based on the current search state. Our empirical resu...