Introducing global constraints in CHIP

Beldiceanu, Nicolas; Contejean, Evelyne

doi:10.1016/0895-7177(94)90127-9

Cited by 227 publications

(208 citation statements)

References 8 publications

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“…Various constraints have been defined over such graph variables (or their preceding specialized models); see for instance the cycle [18], tree [21], path [22,23], minimum spanning tree [24] or spanning tree optimization constraint [25]. In the remainder of this article, we only use the two simple constraints Subgraph(G 1 , G 2 ) (also denoted…”

Section: Cp(graph)mentioning

confidence: 99%

“…Some problems involving undetermined graphs have been formulated using either binary variables, sets ( [14,15]) or integers (successor variables e.g. in [18,19]). CP(Graph) [13] unifies those models by recognizing a common structure: Graph variables are variables whose domain ranges over a set of graphs and as with set variables [20,16], this set of graphs is represented by a graph interval [D(G), D(G)] where D(G), the greatest lower bound (glb) and D(G), the least upper bound (lub) are two graphs with D(G) a subgraph of D(G) (we write D(G) ⊆ D(G)).…”

Section: Cp(graph)mentioning

confidence: 99%

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Combining Two Structured Domains for Modeling Various Graph Matching Problems

Deville

Dooms

Zampelli

2008

Lecture Notes in Computer Science

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Abstract. Graph pattern matching is a central application in many fields. In various areas, the structure of the pattern can only be approximated and exact matching is then too accurate. We focus here on approximations declared by the user within the pattern (optional nodes and forbidden arcs), covering graph/subgraph mono/isomorphism problems. In this paper, we show how the integration of two domains of computation over countable structures, graphs and maps, can be used for modeling and solving various graph matching problems from the simple graph isomorphism to approximate graph matching. To achieve this, we extend map variables allowing the domain and range to be non-fixed and constrained. We describe how such extended maps are designed then realized on top of finite domain and finite set variables with specific propagators. We show how a single monomorphism constraint is sufficient to model and solve those multiples graph matching problems. Furthermore, our experimental results show that our CP approach is competitive with a state of the art algorithm for subgraph isomorphism.

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Section: Cp(graph)mentioning

confidence: 99%

Section: Cp(graph)mentioning

confidence: 99%

Combining Two Structured Domains for Modeling Various Graph Matching Problems

Deville

Dooms

Zampelli

2008

Lecture Notes in Computer Science

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“…Here is the definition of the constraint cumulative (S, D, H, u) from (Beldiceanu and Contejean, 1994): "The cumulative constraint matches directly the single resource scheduling problem, where the S variables correspond to the start of the tasks, the D variables to the duration of the tasks, and the H variable to the heights of the resources that is the amounts of resource used by each task. The natural number u is the total amount of available resource that must be shared at any instant by the different tasks.…”

Section: Examplesmentioning

confidence: 99%

Global Constraints and Filtering Algorithms

Régin¹

2004

Constraint and Integer Programming

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Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP. This chapter is an overview of these two techniques. Some of the most frequently used global constraints are presented. In addition, the filtering algorithms establishing arc consistency for two useful constraints, the alldiff and the global cardinality constraints, are fully detailed. Filtering algorithms are also considered from a theoretical point of view: three different ways to design filtering algorithms are described and the quality of the filtering algorithms studied so far is discussed. A categorization is then proposed. Over-constrained problems are also mentioned and global soft constraints are introduced.

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“…We use the notation a = s a , p a , e a , h a . Given an integer capacity C, a solution to a CuSP satisfies the following constraints: ∀a ∈ A, s a + p a = e a and ∀t ∈ N, ( t∈[sa,ea[,a∈A h a ) ≤ C. In Constraint Programming, the Cumulative(A, C) constraint [3] represents a CuSP. A usual objective is to minimize the makespan, i.e., the latest end among all activities.…”

Section: Introductionmentioning

confidence: 99%