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    ABSTRACT: Scarf’s algorithm (Scarf, H. E. Econometrica 35, 50–69 1967) provides fractional core elements for NTU-games. Biró and Fleiner [4] showed that Scarf’s algorithm can be extended for capacitated NTU-games. In this setting agents can be involved in more than one coalition at a time, cooperations may be performed with different intensities up to some limits, and the contribution of the agents can also differ in a coalition. The fractional stable solutions for the above model, produced by the extended Scarf algorithm, are called stable allocations. In this paper we apply this solution concept for the Hospitals / Residents problem with Couples (HRC). This is one of the most important general stable matching problems due to its relevant applications, also well-known to be NP-hard. We show that if a stable allocation yielded by the Scarf algorithm turns out to be integral then it provides a stable matching for an instance of HRC, so this method can be used as a heuristic. In an experimental study, we compare this method with other heuristics constructed for HRC that have been applied in practice in the American and Scottish resident allocation programs, respectively. Our main finding is that the Scarf algorithm outperforms all the other known heuristics when the proportion of couples is high.
    Full-text · Article · Nov 2015 · Annals of Mathematics and Artificial Intelligence

  • No preview · Article · Jun 2014 · Theoretical Computer Science
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    ABSTRACT: The biochemical paradigm is well-suited for modelling autonomous systems and new programming languages are emerging from this approach. However, in order to validate such programs, we need to define precisely their semantics and to provide verification techniques. In this paper, we consider a higher-order biochemical calculus that models the structure of system states and its dynamics thanks to rewriting abstractions, namely rules and strategies. We extend this calculus with a runtime verification technique in order to perform automatic discovery of property satisfaction failure. The property specification language is a subclass of LTL safety and liveness properties.
    Full-text · Article · Dec 2013 · Electronic Notes in Theoretical Computer Science
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