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27
ArcConsistency and ArcConsistency Again
 Artificial Intelligence
, 1994
"... Constraint networks are known as a useful way to formulate problems such as design, scene labeling, temporal reasoning, and more recently natural language parsing. The problem of the existence of solutions in a constraint network is NPcomplete. Hence, consistency techniques have been widely studied ..."
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Cited by 151 (12 self)
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Constraint networks are known as a useful way to formulate problems such as design, scene labeling, temporal reasoning, and more recently natural language parsing. The problem of the existence of solutions in a constraint network is NPcomplete. Hence, consistency techniques have been widely studied to simplify constraint networks before or during the search of solutions. Arcconsistency is the most used of them. Mohr and Henderson [Moh&Hen86] have proposed AC4, an algorithm having an optimal worstcase time complexity. But it has two drawbacks: its space complexity and its average time complexity. In problems with many solutions, where the size of the constraints is large, these drawbacks become so important that users often replace AC4 by AC3 [Mac&Fre85], a nonoptimal algorithm. In this paper, we propose a new algorithm, AC6, which keeps the optimal worstcase time complexity of AC4 while working out the drawback of space complexity. More, the average time complexity of AC6 is optimal for constraint networks where nothing is known about the semantic of the constraints. At the end of the paper, experimental results show how much AC6 outperforms AC3 and AC4. 1.
Improved CLP Scheduling with Task Intervals
, 1994
"... In this paper we present a new technique that can be used to improve performance of job scheduling with a constraint programming language. We show how, by focusing on some special sets of tasks, one can bring CLP in the same range of efficiency as traditional OR algorithms on a classical benchmark ( ..."
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Cited by 99 (6 self)
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In this paper we present a new technique that can be used to improve performance of job scheduling with a constraint programming language. We show how, by focusing on some special sets of tasks, one can bring CLP in the same range of efficiency as traditional OR algorithms on a classical benchmark (MT10 [MT63]), thus making CLP both a flexible and an efficient technique for such combinatorial problems. We then present our programming methodology which we have successfully used on many problems, and draw conclusions on what features constraint programming languages should offer to allow its use. 1. Introduction Reallife scheduling problems are often the composition of various wellidentified hard problems. In the previous years, we have worked on applications such as tasktechnician assignments [CK92] or staff timetable scheduling [CGL93] and developed a methodology for solving such problems with an extensible constraint logic programming language. In both cases we have applied the s...
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 51 (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.
Fast Local Search and Guided Local Search and Their Application to British Telecom’s Workforce Scheduling Problem
, 1997
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An efficient arc consistency algorithm for a class of csp problems
, 1991
"... Consistency Techniques have been studied extensively in the past as a way of tackling Constraint Satisfaction Problems (CSP). In particular various arc consistency algorithms have been proposed, originating from Waltz's filtering algorithm [20] and culminating in the optimal algorithm AC4 of M ..."
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Cited by 44 (1 self)
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Consistency Techniques have been studied extensively in the past as a way of tackling Constraint Satisfaction Problems (CSP). In particular various arc consistency algorithms have been proposed, originating from Waltz's filtering algorithm [20] and culminating in the optimal algorithm AC4 of Mohr and Henderson [13]. AC4 runs in 0(ed 2) in the worst case where e is the number of arcs (or constraints) and d is the site of the largest domain. Being applicable to the whole class of (binary) CSP, these algorithms do not take into account the semantics of constraints. In this paper, we present a new generic arc consistency algorithm AC5. The algorithm is parametrised on two specified procedures and can be instantiated to reduce to AC3 and AC4. More important, AC5 can be instantiated to produce an 0(ed) algorithm for two important classes of constraints: functional and monotonic constraints. We also show that AC5 has an important application in Constraint Logic Programming over Finite Domains [18]. The kernel of the constraintsolver for such a programming language is an arc consistency algorithm for a set of basic constraints. We prove that AC5, in conjunction with node consistency, provides a decision procedure for these constraints running in time 0(ed). 1
Extending GENET for NonBinary CSP’s
, 1995
"... GENET has been shown to be efficient and effective on certain hard or large constraint satasfaction problems. Although GENET has been enhanced to handle also the atmost and illegal constraints in addition to binary constraints, it is deficient in handling nonbinary constraints in general. In thi ..."
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Cited by 22 (4 self)
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GENET has been shown to be efficient and effective on certain hard or large constraint satasfaction problems. Although GENET has been enhanced to handle also the atmost and illegal constraints in addition to binary constraints, it is deficient in handling nonbinary constraints in general. In this paper, we present EGENET, an extended GENET. EGENET features a convergence and learning procedure similar to that of GENET and a generic representation scheme for general constraints, which range from disjunctive constraints to nonlinear constraints to symbolic constraants. We have implemented an eficient prototype of E GENET for singleprocessor machines. Benchmarking results confirms the eficiency and flexibility of EGENET. Our implementation also compares well against CHIP, PROCLANN, and GENET.
Terminological Reasoning with Constraint Handling Rules
, 1994
"... Terminological knowledge representation formalisms in the tradition of kloneenable one to define the relevant concepts of a problem domain and their interaction in a structured and wellformed way. Recently, M. SchmidtSchauß and G. Smolka proposed a new methodology for constructing sound and compl ..."
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Cited by 18 (6 self)
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Terminological knowledge representation formalisms in the tradition of kloneenable one to define the relevant concepts of a problem domain and their interaction in a structured and wellformed way. Recently, M. SchmidtSchauß and G. Smolka proposed a new methodology for constructing sound and complete inference algorithms for terminological logics. The consistency test of assertions is the basis for all terminological reasoning services. We propose constraint handling rules (CH rules) as an implementation language for terminological reasoning. CH rulesare a flexible means to implement `userdefined' constraints on top of existing host languages like Prolog and Lisp. The implementation results in a natural combination of three layers: (i) a constraint layer that reasons in wellunderstood domains such as rationals or finite domains, (ii) a terminological layer providing a tailored, validated vocabulary on which (iii) the application layer can rely. As an application example, a configur...
Constraint Satisfaction with an ObjectOriented Knowledge Representation Language
, 1994
"... This paper gives a detailed presentation of constraint satisfaction in the hybrid LAURE language. LAURE is an objectoriented language for Artificial Intelligence (AI) applications which allows the user to combine rules, constraints and methods that cooperate on the same objects in the same program. ..."
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Cited by 14 (3 self)
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This paper gives a detailed presentation of constraint satisfaction in the hybrid LAURE language. LAURE is an objectoriented language for Artificial Intelligence (AI) applications which allows the user to combine rules, constraints and methods that cooperate on the same objects in the same program. We illustrate why this extensibility is necessary to solve some large and difficult problems by presenting a reallife application of LAURE. We describe the syntax and the various modes in which constraints may be used, as well as the tools that are proposed by LAURE to extend constraint resolution. The resolution strategy as well as some implementation details are given to explain how we obtain good performances.
Extending a GeneralPurpose Algebraic Modeling Language to Combinatorial Optimization: A Logic Programming Approach
 IN ADVANCES IN COMPUTATIONAL AND STOCHASTIC OPTIMIZATION, LOGIC PROGRAMMING, AND HEURISTIC SEARCH: INTERFACES IN COMPUTER SCIENCE AND OPERATIONS RESEARCH
, 1998
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New Constructs for the Description of Combinatorial Optimization Problems in Algebraic Modeling Languages
 Computational Optimization and Applications
, 1996
"... Algebraic languages are at the heart of many successful optimization modeling systems, yet they have been used with only limited success for combinatorial (or discrete) optimization. We show in this paper, through a series of examples, how an algebraic modeling language might be extended to help wit ..."
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Cited by 9 (4 self)
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Algebraic languages are at the heart of many successful optimization modeling systems, yet they have been used with only limited success for combinatorial (or discrete) optimization. We show in this paper, through a series of examples, how an algebraic modeling language might be extended to help with a greater variety of combinatorial optimization problems. We consider specifically those problems that are readily expressed as the choice of a subset from a certain set of objects, rather than as the assignment of numerical values to variables. Since there is no practicable universal algorithm for problems of this kind, we explore a hybrid approach that employs a generalpurpose subset enumeration scheme together with problemspecific directives to guide an efficient search. Published as: