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Generalizzazioni di matroidi

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Ottimizzazione Combinatoria

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Riassunto

Esistono diverse generalizzazioni interessanti dei matroidi. Nella Sezione 13.1 abbiamo già visto i sistemi di indipendenza, che si ottengono tralasciando l’assioma (M3). Nella Sezione 14.1 consideriamo i greedoidi, che si ottengono invece rimuovendo la (M2). Inoltre, alcuni politopi legati ai matroidi e alle funzioni submodulari, chiamati polimatroidi, portano a delle generalizzazioni forti di teoremi importanti; li discuteremo nella Sezione 14.2. Nelle Sezioni 14.3 e 14.4 consideriamo due approcci al problema di minimizzare una funzione submodulare qualunque: uno che usa il Metodo dell’Ellissoide e l’altro che usa un algoritmo combinatorio. Nella Sezione 14.5, mostriamo un algoritmo più semplice per il caso speciale di funzioni submodulari simmetriche.

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Authors and Affiliations

  1. Research Institute for Discrete Mathematics, University of Bonn, Germany

    Bernhard Korte & Jens Vygen

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  1. Bernhard Korte
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  2. Jens Vygen
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Korte, B., Vygen, J. (2011). Generalizzazioni di matroidi. In: Ottimizzazione Combinatoria. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-1523-4_14

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