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Alberi di supporto e arborescenze

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Ottimizzazione Combinatoria

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Riassunto

Si consideri una compagnia telefonica che vuole affittare un sottoinsieme dei suoi esistenti, ognuno dei quali connette due città. I cavi affittati dovrebbero essere sufficienti a connettere tutte le città e dovrebbero essere il più economici possibile. È naturale in questo caso rappresentare la rete telefonica con un grafo: i vertici rappresentano le città e gli archi i cavi. Per il Teorema 2.4 i sottografi connessi di supporto di cardinalità minima sono i suoi alberi di supporto. Cerchiamo dunque un albero di supporto di peso minimo, in cui diciamo che il sottografo T di un grafo G con pesi c: E(G) → ℝ ha peso c(E(T)) = ∑e∈E(T)c(e). Indicheremo con c(e) il costo dell’arco e.

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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). Alberi di supporto e arborescenze. In: Ottimizzazione Combinatoria. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-1523-4_6

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