By Helmut Simonis

This booklet constitutes the lawsuits of the foreign convention at the Integration of synthetic Intelligence (AI) and Operations examine (OR) innovations in Constraint Programming, CPAIOR 2014, held in Cork, eire, in may perhaps 2014. The 33 papers provided during this quantity have been rigorously reviewed and chosen from 70 submissions. The papers concentrate on constraint programming and worldwide constraints; scheduling modelling; encodings and SAT logistics; MIP; CSP and complexity; parallelism and seek; and knowledge mining and computing device learning.

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**Additional resources for Integration of AI and OR Techniques in Constraint Programming: 11th International Conference, CPAIOR 2014, Cork, Ireland, May 19-23, 2014. Proceedings**

**Example text**

Salvagnin Fig. 1. Assignment structure and the constraints in a pair of matching clusters (q1 , q2 ) corresponds to the rows and columns, respectively, of this matrix, see Figure 1. Once a matching pair of cluster is found, it is removed from Q and the process continues until all pairs have been considered. Details are depicted in Algorithm 1. Note that the described detection algorithm is slightly more general than needed, since it can detect more than one assignment substructures. The second step constructs a weighted dependency graph G = (V, E, w) between the variables of the formulation, along with a topological order O on the nodes of G, and is based on row counts.

In: Walsh, T. ) CP 2001. LNCS, vol. 2239, pp. 225–239. Springer, Heidelberg (2001) 7. : The Stable Marriage Problem: Structure and Algorithms. The MIT Press (1989) 8. : An eﬃcient algorithm for the “stable roommates” problem. J. Algorithms 6(4), 577–595 (1985) 9. : Optimal Stable Marriage. In: Encyclopedia of Algorithms. Springer (2008) 10. : Consistency in networks of relations. Artiﬁcial Intelligence 8, 99–118 (1977) 11. : Algorithmics of Matching under Preferences. Theoretical Computer Science, vol.

Therefore, if a value is removed from the domain of ai , O(n) constraints will be revised. This can occur n times for an agent, and since there are n agents this results in O(n3 ) complexity, assuming it takes O(1) time to revise a constraint as above. With a specialized n-ary constraint we can improve upon this. We can eliminate the above redundancy by revising only the domains of agents that must be aﬀected by a change in another variable’s domain. There are ﬁve possible changes that can occur to the domain of an agent and these are: Stable Roommates and Constraint Programming – – – – – 21 the upper bound of a variable decreases (Algorithm 1) the lower bound of a variable increases (Algorithm 2) a variable looses a value (Algorithm 3) a variable is instantiated (Algorithm 4) the constraint is initially posted (Algorithm 5) Presented below are the algorithms that address these ﬁve cases and the actual choco/Java implementation (Listing 2, with imports removed for brevity).