From 064eeabad5758668a421d131635552334bda1f55 Mon Sep 17 00:00:00 2001 From: Paul ALNET Date: Sun, 4 Jun 2023 10:42:04 +0200 Subject: [PATCH] tex: list variables --- latex/content.tex | 18 +++++++++++++++++- 1 file changed, 17 insertions(+), 1 deletion(-) diff --git a/latex/content.tex b/latex/content.tex index 2003c8f..d6664d1 100644 --- a/latex/content.tex +++ b/latex/content.tex @@ -114,15 +114,31 @@ we store each item in the next bin if it fits, otherwise we open a new bin. will be of random sizes between $ 0 $ and $ 1 $. We will run X simulations % TODO with 10 packets. -\subsubsection{Variables used in models} +\subsection{Variables used in models} +We use the following variables in our algorithms and models : +\begin{itemize} + + \item $ U_n $ : the size of the $ n $-th item. $ (U_n)_{n \in \mathbb{N}} $ + denotes the mathematical sequence of random variables of uniform + distribution on $ [0, 1] $ representing the items' sizes. + + \item $ T_i $ : the number of items in the $ i $-th bin. + + \item $ V_i $ : the size of the first item in the $ i $-th bin. + + \item $ H_n $ : the number of bins required to store $ n $ items. + +\end{itemize} \cite{hofri:1987} % TODO mettre de l'Histoire \section{Next Fit Dual Bin Packing algorithm} +The variables used are the same as for NFBP. + \subsection{La giga demo} Let $ k \in \mathbb{N} $. Let $ (U_n)_{n \in \mathbb{N}} $ be a sequence of