Generalized Arc Consistency for Positive Table Constraints

Lecoutre, Christophe; Szymanek, Radosław

doi:10.1007/11889205_22

Cited by 45 publications

(68 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Proof It was shown in [16] that an optimal SAC transformation can be found, for any VCSP, by first propagating infinite costs using a standard generalized arc consistency algorithm [40,43] and then by solving a linear program. (A more detailed description of this algorithm is given below).…”

Section: Sfm Via Linear Programmingmentioning

confidence: 99%

“…This necessarily converges since each cost φ σ (x) can be increased to ∞ at most once. In fact, the propagation of infinite costs by SAC operations in the VCSP P = V, D, C can be achieved by establishing generalized arc consistency [43] in the feasibility CSP Feas(P) = V, D, { σ, Feas(φ) : σ, φ ∈ C} , a standard operation in Constraint Programming for which efficient algorithms have been developed [40]. Alternatively, the constraints of Feas(P) can be decomposed into their binary projections and a standard arc consistency algorithm applied [1].…”

Section: Sfm Via Linear Programmingmentioning

confidence: 99%

See 1 more Smart Citation

Minimization of Locally Defined Submodular Functions by Optimal Soft Arc Consistency

Cooper

2008

Constraints

View full text Add to dashboard Cite

Submodular function minimization is a polynomially solvable combinatorial problem. Unfortunately the best known general-purpose algorithms have highorder polynomial time complexity. In many applications the objective function is locally defined in that it is the sum of cost functions (also known as soft or valued constraints) whose arities are bounded by a constant. We prove that every valued constraint satisfaction problem with submodular cost functions has an equivalent instance on the same constraint scopes in which the actual minimum value of the objective function is rendered explicit. Such an equivalent instance is the result of establishing optimal soft arc consistency and can hence be found by solving a linear program. From a practical point of view, this provides us with an alternative algorithm for minimizing locally defined submodular functions. From a theoretical point of view, this brings to light a previously unknown connection between submodularity and soft arc consistency.

show abstract

Section: Sfm Via Linear Programmingmentioning

confidence: 99%

Section: Sfm Via Linear Programmingmentioning

confidence: 99%

Minimization of Locally Defined Submodular Functions by Optimal Soft Arc Consistency

Cooper

2008

Constraints

View full text Add to dashboard Cite

show abstract

“…Unfortunately, achieving generalised arc consistency (GAC) [4,15,16] on the reformulation is not equivalent to achieving GAC on the original constraint. Arc-consistency is preserved only in the case of dependencies between pairs of variables.…”

Section: Definition 4 (Minimal Reformulation)mentioning

confidence: 99%

Reformulating Positive Table Constraints Using Functional Dependencies

Cambazard

O’Sullivan

2008

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Constraints that are defined by tables of allowed tuples of assignments are common in constraint programming. In this paper we present an approach to reformulating table constraints of large arity into a conjunction of lower arity constraints. Our approach exploits functional dependencies. We study the complexity of finding reformulations that either minimize the memory size or arity of a constraint using a set of its functional dependencies. We also present an algorithm to compute such reformulations. We show that our technique is complementary to existing approaches for compressing extensional constraints.

show abstract

“…[10,1,12,6]. For each variable value pair (x, a), the index data structure has an array of the indexes of the tuples with value a for x.…”

Section: Introductionmentioning

confidence: 99%

“…The next data structure is semantically equivalent to the index of [12]. More formally, for a given table constraint c, FS and next satisfy the following invariant (called FS-invariant) before dequeuing an element from Q.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Filtering Algorithm for Table Constraints

Mairy

Hentenryck

Deville

2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Filtering algorithms for table constraints are constraint-based, which means that the propagation queue only contains information on the constraints that must be reconsidered. This paper proposes four efficient value-based algorithms for table constraints, meaning that the propagation queue also contains information on the removed values. One of these algorithms (AC5TC-Tr) is proved to have an optimal time complexity of O(r.t + r.d) per table constraint. Experimental results show that, on structured instances, all our algorithms are two or three times faster than the state of the art STR2+ and MDD c algorithms.

show abstract

Generalized Arc Consistency for Positive Table Constraints

Cited by 45 publications

References 6 publications

Minimization of Locally Defined Submodular Functions by Optimal Soft Arc Consistency

Minimization of Locally Defined Submodular Functions by Optimal Soft Arc Consistency

Reformulating Positive Table Constraints Using Functional Dependencies

An Optimal Filtering Algorithm for Table Constraints

Contact Info

Product

Resources

About