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An Order-theoretic Framework for the Greedy Algorithm with Applications to the Core and Weber Set of Cooperative Games

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Abstract

An algebraic model generalizing submodular polytopes is presented, where modular functions on partially ordered sets take over the role of vectors in R n. This model unifies various generalizations of combinatorial models in which the greedy algorithm and the Monge algorithm are successful and generalizations of the notions of core and Weber set in cooperative game theory.

As a further application, we show that an earlier model of ours as well as the algorithmic model of Queyranne, Spieksma and Tardella for the Monge algorithm can be treated within the framework of usual matroid theory (on unordered ground-sets), which permits also the efficient algorithmic solution of the intersection problem within this model.

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Authors and Affiliations

  1. Mathematical Institute, Center for Applied Computer Science, University of Cologne, Weyertal 80, D-50931, Köln, Germany

    Ulrich Faigle

  2. Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Walter Kern

Authors
  1. Ulrich Faigle
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  2. Walter Kern
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Faigle, U., Kern, W. An Order-theoretic Framework for the Greedy Algorithm with Applications to the Core and Weber Set of Cooperative Games. Order 17, 353–375 (2000). https://doi.org/10.1023/A:1006406424957

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