tex: list variables
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@ -114,15 +114,31 @@ we store each item in the next bin if it fits, otherwise we open a new bin.
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will be of random sizes between $ 0 $ and $ 1 $. We will run X simulations % TODO
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will be of random sizes between $ 0 $ and $ 1 $. We will run X simulations % TODO
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with 10 packets.
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with 10 packets.
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\subsubsection{Variables used in models}
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\subsection{Variables used in models}
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We use the following variables in our algorithms and models :
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\begin{itemize}
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\item $ U_n $ : the size of the $ n $-th item. $ (U_n)_{n \in \mathbb{N}} $
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denotes the mathematical sequence of random variables of uniform
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distribution on $ [0, 1] $ representing the items' sizes.
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\item $ T_i $ : the number of items in the $ i $-th bin.
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\item $ V_i $ : the size of the first item in the $ i $-th bin.
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\item $ H_n $ : the number of bins required to store $ n $ items.
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\end{itemize}
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\cite{hofri:1987}
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\cite{hofri:1987}
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% TODO mettre de l'Histoire
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% TODO mettre de l'Histoire
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\section{Next Fit Dual Bin Packing algorithm}
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\section{Next Fit Dual Bin Packing algorithm}
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The variables used are the same as for NFBP.
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\subsection{La giga demo}
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\subsection{La giga demo}
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Let $ k \in \mathbb{N} $. Let $ (U_n)_{n \in \mathbb{N}} $ be a sequence of
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Let $ k \in \mathbb{N} $. Let $ (U_n)_{n \in \mathbb{N}} $ be a sequence of
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