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Generalizing AllDifferent: The SomeDifferent constraint. (English) Zbl 1160.68561
Benhamou, Frédéric (ed.), Principles and practice of constraint programming – CP 2006. 12th international conference, CP 2006, Nantes, France, September 25–29, 2006. Proceedings. Berlin: Springer (ISBN 978-3-540-46267-5/pbk). Lecture Notes in Computer Science 4204, 468-483 (2006).
Summary: We introduce the SomeDifferent constraint as a generalization of AllDifferent. SomeDifferent requires that values assigned to some pairs of variables will be different. It has many practical applications. For example, in workforce management, it may enforce the requirement that the same worker is not assigned to two jobs which are overlapping in time. Propagation of the constraint for hyper-arc consistency is NP hard. We present a propagation algorithm with worst case time complexity $$O(n^{3}\beta ^{n})$$ where $$n$$ is the number of variables and $$\beta \approx 3.5$$ (ignoring a trivial dependence on the representation of the domains). We also elaborate on several heuristics which greatly reduce the algorithm’s running time in practice. We provide experimental results, obtained on a real-world workforce management problem and on synthetic data, which demonstrate the feasibility of our approach.
For the entire collection see [Zbl 1141.68004].

##### MSC:
 68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 68Q25 Analysis of algorithms and problem complexity
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