A Sufficient Condition for Backtrack-Free Search

Freuder, Eugene C.

doi:10.1145/322290.322292

Cited by 491 publications

(220 citation statements)

References 8 publications

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“…Our results unify and generalize several previously studied classes of problems, including tree-structured problems [25], problems with max-closed constraints [36], problems where the constraints are preserved by a set function [21], and problems with the broken-triangle property [18].…”

Section: Summary and Related Worksupporting

confidence: 79%

“…If every instance in a class defined by a structural restriction is decided by GAC it means that we can apply arbitrary constraints over the same scopes and the result will still be decided by GAC. It is well-known that any binary CSP instance where the constraint scopes form a tree is decided by GAC [25]. To obtain a simple generalisation of this result to non-binary CSP instances we need to identify a suitable generalisation of the notion of a tree.…”

Section: Structural Restrictionsmentioning

confidence: 99%

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The power of propagation: when GAC is enough

Cohen

Jeavons

2016

Constraints

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Considerable effort in constraint programming has focused on the development of efficient propagators for individual constraints. In this paper, we consider the combined power of such propagators when applied to collections of more than one constraint. In particular we identify classes of constraint problems where such propagators can decide the existence of a solution on their own, without the need for any additional search. Sporadic examples of such classes have previously been identified, including classes based on restricting the structure of the problem, restricting the constraint types, and some hybrid examples. However, there has previously been no unifying approach which characterises all of these classes: structural, language-based and hybrid. In this paper we develop such a unifying approach and embed all the known classes into a common framework. We then use this framework to identify a further class of problems that can be solved by propagation alone.

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Section: Summary and Related Worksupporting

confidence: 79%

Section: Structural Restrictionsmentioning

confidence: 99%

The power of propagation: when GAC is enough

Cohen

Jeavons

2016

Constraints

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show abstract

“…The more difficult the CSP, the larger is its search space, and the more advantageous it is to enforce consistency properties of higher levels. In fact, Freuder provided a sufficient condition for guaranteeing a backtrack-free search that links the level of consistency to a structural parameter of the CSP [7]. However, enforcing higher-level consistencies may add constraints and modify the structure of the problem.…”

Section: Consistency Properties and Algorithmsmentioning

confidence: 99%

Revisiting Neighborhood Inverse Consistency on Binary CSPs

Woodward

Karakashian

Choueiry

et al. 2012

Lecture Notes in Computer Science

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Abstract. Our goal is to investigate the definition and application of strong consistency properties on the dual graphs of binary Constraint Satisfaction Problems (CSPs). As a first step in that direction, we study the structure of the dual graph of binary CSPs, and show how it can be arranged in a triangle-shaped grid. We then study, in this context, Relational Neighborhood Inverse Consistency (RNIC), which is a consistency property that we had introduced for non-binary CSPs [17]. We discuss how the structure of the dual graph of binary CSPs affects the consistency level enforced by RNIC. Then, we compare, both theoretically and empirically, RNIC to Neighborhood Inverse Consistency (NIC) and strong Conservative Dual Consistency (sCDC), which are higherlevel consistency properties useful for solving difficult problem instances. We show that all three properties are pairwise incomparable.

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“…The ordering may be either a static ordering, or dynamic ordering. Examples of static ordering heuristics are minimum width [12] and maximum degree [7], in which the order of the variables is specified before the search begins, and it is not changed thereafter. An example of dynamic ordering heuristic is minimum remaining values [17], in which the choice of next variable to be considered depends on the current state of the search.…”

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confidence: 99%

A non-binary constraint ordering heuristic for constraint satisfaction problems

Salido

2008

Applied Mathematics and Computation

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Nowadays many real problems can be modelled as Constraint Satisfaction Problems (CSPs). A search algorithm for constraint programming requires an order in which variables and values should to be considered. Choosing the right order of variables and values can noticeably improve the efficiency of constraint satisfaction. Furthermore, the order in which constraints are studied can improve efficiency, particularly in problems with non-binary constraints. In this paper, we present a preprocess heuristic called Constraint Ordering Heuristic (COH) that studies the constrainedness of the scheduling problem and mainly classifies the constraints so that the tightest ones are studied first. Thus, constrainedness can be known in advance and overall inconsistencies can be found earlier and the number of constraint checks can significantly be reduced.Keywords: Heuristic Search, Constraint ordering, Non-binary Constraints, Constrainedness.1 2 IntroductionNowadays, many real problems can be efficiently modelled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. Some problems can be modelled naturally using non-binary constraints [26,19,8]. Although, researchers have traditionally focused on binary constraints [24], the need to address issues regarding non-binary constraints has recently started to be widely recognized in the constraint satisfaction literature. Thus, to define heuristics to solve non-binary CSPs becomes relevant.One approach to solving CSPs is to use a depth-first backtrack search algorithm [5]. While the worst-case complexity of backtrack search is exponential, several heuristics to reduce its average-case complexity have been proposed in the literature [6]. However, determining which algorithms are superior to others remains difficult. Theoretical analysis provides worst-case guarantees which often do not reflect average performance. For instance, a backtracking-based algorithm that incorporates features such as variable ordering heuristics will often in practice have substantially better performance than a simpler algorithm without this feature [17], and yet the two share the same worst-case complexity. Similarly, one algorithm may be better than another on problems with a certain characteristic, and worse on another category of problem. Ideally, we would be able to identify this characteristic in advance and use it to guide our choice of algorithm.Many of the heuristics that improve backtracking-based algorithms are based on variable ordering and value ordering [20, 2], due to the additivity of the variables and values. However, constraints are also considered to be additive, that is, the order of imposition of constraints does not matter, all that matters is that the conjunction of constraints be satisfied [2].Thus, a real problem can be modelled as a CSP, and using some of the current ordering heuristics, it can be solved in a more efficient way by some of the backtracking-based search algorithms (Figure 1).In spite of the additivity of constraints, only...

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A Sufficient Condition for Backtrack-Free Search

Cited by 491 publications

References 8 publications

The power of propagation: when GAC is enough

The power of propagation: when GAC is enough

Revisiting Neighborhood Inverse Consistency on Binary CSPs

A non-binary constraint ordering heuristic for constraint satisfaction problems

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