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On the use of binary decision diagrams for solving problems on simple games

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  • Berghammer, Rudolf
  • Bolus, Stefan

Abstract

Simple games are yes/no cooperative games which arise in many practical applications. Recently, we have used reduced ordered binary decision diagrams and quasi-reduced ordered binary decision diagrams (abbreviated as Robdds and Qobdds, respectively) for the representation of simple games and for the computation of some power indices. In the present paper, we continue this work. We show how further important computational problems on simple games can be solved using Qobdds, viz. the identification of some key players, the computation of the desirability relation on individuals, the test whether a simple game is proper and strong, respectively, and the computation of Qobdd-representations for the sets of all minimal winning coalitions, all shift-minimal winning coalitions and all blocking coalitions, respectively. Applications of these solutions include the computation of recent power indices based on shift-minimal winning coalitions and the test for linear separability of a directed simple game.

Suggested Citation

  • Berghammer, Rudolf & Bolus, Stefan, 2012. "On the use of binary decision diagrams for solving problems on simple games," European Journal of Operational Research, Elsevier, vol. 222(3), pages 529-541.
  • Handle: RePEc:eee:ejores:v:222:y:2012:i:3:p:529-541
    DOI: 10.1016/j.ejor.2012.04.015
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    References listed on IDEAS

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    1. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2010. "Applying relation algebra and RelView to measures in a social network," European Journal of Operational Research, Elsevier, vol. 202(1), pages 182-195, April.
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    Cited by:

    1. Heradio, Ruben & Perez-Morago, Hector & Alférez, Mauricio & Fernandez-Amoros, David & Alférez, Germán H., 2016. "Augmenting measure sensitivity to detect essential, dispensable and highly incompatible features in mass customization," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1066-1077.
    2. Molinero, Xavier & Riquelme, Fabián & Serna, Maria, 2015. "Forms of representation for simple games: Sizes, conversions and equivalences," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 87-102.
    3. Molinero, Xavier & Riquelme, Fabián & Serna, Maria, 2015. "Cooperation through social influence," European Journal of Operational Research, Elsevier, vol. 242(3), pages 960-974.

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