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Correzione Flow network

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L'immagine 3_2_2_2 del flow network è stata cambiata e l'esempio teorico corretto che era sbagliato
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meschio94 2022-02-12 13:40:33 +01:00
parent cb74fb50c9
commit a93d501800
8 changed files with 408 additions and 406 deletions
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\BOOKMARK [2][-]{subsection.6.15}{NP problem}{section.6}% 69 \BOOKMARK [2][-]{subsection.6.15}{\376\377\000N\000P\000\040\000p\000r\000o\000b\000l\000e\000m}{section.6}% 69

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@ -24,7 +24,7 @@
\title{Gran Compendio OLI} \title{Gran Compendio OLI}
\author{\href{https://github.com/meschio94/Gran-Compendio-OLI}{Meschio}} \author{\href{https://github.com/meschio94/Gran-Compendio-OLI}{Meschio}}
\date{2021\\V1.2.2} \date{2021\\V1.2.3}
\begin{document} \begin{document}
\maketitle \maketitle
@ -875,7 +875,7 @@ Soluzione:
\item il flusso massimo che posso avere in uscita sul nodo t, è 5.\\ \item il flusso massimo che posso avere in uscita sul nodo t, è 5.\\
osservando l'immagine sopra, nel quale ho rimosso i flussi passanti e lasciato solo i flussi di capacita, notiamo che malgrado il nodo t abbia un upperbound massimo di 7, in realtà i suoi archi entranti che arrivano dal nodo 3 e 4, possono sostenere realisticamente e rispettivamente una capacità reale di uscita di 4 per il nodo 3, e di 2 per il nodo 4, dobbiamo anche notare che un nodo uscente di 3 finisce giusto nel nodo 4, quindi abbiamo nel best case scenario che il nodo 3 e 4 possono approvvigionare rispettivamente 3 dall'arco superiore e 2 dall'arco inferiore. osservando l'immagine sopra, nel quale ho rimosso i flussi passanti e lasciato solo i flussi di capacita, notiamo che malgrado il nodo t abbia un upperbound massimo di 7, in realtà i suoi archi entranti che arrivano dal nodo 3 e 4, possono sostenere realisticamente e rispettivamente una capacità reale di uscita di 4 per il nodo 3, e di 2 per il nodo 4, dobbiamo anche notare che un nodo uscente di 3 finisce giusto nel nodo 4, quindi abbiamo nel best case scenario che il nodo 3 e 4 possono approvvigionare rispettivamente 3 dall'arco superiore e 2 dall'arco inferiore.
\item Ricordando il teorema di Ford-Fulkerson: "il valore di un flusso accettabile di un flusso massimo in un grafo è uguale alla capacità di un taglio di minima capacità", ovvero, se io faccio un taglio tra 2 nodi, che hanno capacità minima in uscita (archi uscenti), trovo la capacità massima che posso avere nel mio network, in questo caso, se prendo i nodi ($1,2$), avrò come archi uscenti {$(1,3),(1,4),(2,3)$}: \item Ricordando il teorema del Max-flow min-cut: "Il valore massimo di flusso tra $s$ e $t$ equivale sempre al peso del taglio minimo $s-t$", ovvero, devo effettuare un taglio che includa il numero minimo di archi, e che separi il nodo $s$ da $t$, il flusso che scorre in quel taglio, è il flusso massimo che il network può supportare, da immagine qua sotto, vediamo l'esempio separando vicino al nodo $s$ con la linea tratteggiata blu, tale esempio può funzionare anche vicino al nodo $t$, considerando che in questa immagine anche questo taglio avrebbe due archi, ed effettivamente sommando il flusso del taglio (i numeri evidenziati in rosso) il valore di flusso massimo è $4$!:
\begin{center} \begin{center}
\raisebox{-.5\height}{\includegraphics[width=6cm]{immagini/grafi/3_2_2_2.jpg}} \raisebox{-.5\height}{\includegraphics[width=6cm]{immagini/grafi/3_2_2_2.jpg}}
\end{center} \end{center}

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