By Christophe Lecoutre(auth.), Narendra Jussien(eds.)
A massive problem in constraint programming is to increase effective regular techniques to resolve cases of the constraint pride challenge (CSP). With this goal in brain, this booklet presents an obtainable synthesis of the author's examine and paintings during this quarter, divided into 4 major subject matters: illustration, inference, seek, and studying. the implications received and reproduced during this ebook have a large applicability, whatever the nature of the matter or the restrictions concerned, making it an exceptionally straightforward source for these interested by this field.Content:
Chapter 1 Constraint Networks (pages 39–91):
Chapter 2 Random and based Networks (pages 93–131):
Chapter three Consistencies (pages 137–184):
Chapter four regularly occurring GAC Algorithms (pages 185–237):
Chapter five Generalized Arc Consistency for desk Constraints (pages 239–286):
Chapter 6 Singleton Arc Consistency (pages 287–317):
Chapter 7 direction and twin Consistency (pages 319–354):
Chapter eight back down seek (pages 359–390):
Chapter nine Guiding seek towards Conflicts (pages 391–430):
Chapter 10 Restarts and Nogood Recording (pages 431–458):
Chapter eleven State?based Reasoning (pages 459–494):
Chapter 12 Symmetry Breaking (pages 495–530): Christophe Lecoutre and Sebastien Tabary
Chapter A Mathematical heritage (pages 531–539):
Chapter B XML illustration of Constraint Networks (pages 541–545):
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Additional resources for Constraint Networks: Techniques and Algorithms
In the 3-queens instance we can see that both c12 and c12 independently support (x1 , 2).
We now introduce the density of a constraint network since this is a notion that can be related to (hyper)graphs. – [Density] Let P ∈ Pk be a constraint network (only involving constraints of arity k). The density of (the constraint hypergraph associated with) P is equal to e/(nk ). For k = 2 (the usual case) the network density is equal to 2e/(n2 − n). For example, for a binary network involving 10 variables and 15 constraints, the density is 30/90 ≈ 33%. 58 Constraint Networks Finally, the compatibility hypergraph, also called micro-structure [JÉG 93], associated with a normalized constraint network P contains one vertex per v-value of P and one hyperedge per constraint support.
Constraint Networks 65 By deﬁnition, a sub-network P of P is such that ∀c ∈ cons(P ), scp(c) ⊆ vars(P ) since P is a constraint network. Also, the state of variables and constraints is unchanged: we have ∀x ∈ vars(P ), domP (x) = domP (x) and ∀c ∈ cons(P ), relP (c) = relP (c). 13 is an illustration of a sub-network. 13. 3. Examples of constraint networks We now give several examples of problems that can easily be represented using the formalism of constraint networks. Both for simplicity and for entertainment, all these problems correspond to logic puzzles.