diff --git a/latex/content.tex b/latex/content.tex index 374186c..7399933 100644 --- a/latex/content.tex +++ b/latex/content.tex @@ -145,10 +145,22 @@ Mathematically, the NFBP algorithm imposes the following constraint on the first We implemented the NFBP algorithm in Python \footnotemark, for its ease of use and broad recommendation. We used the \texttt{random} library to generate random numbers between $ 0 $ and $ 1 $ and \texttt{matplotlib} to plot the -results. +results in the form of histograms. We ran $ R = 10^6 $ simulations with +$ N = 10 $ different items each. \footnotetext{The code is available in Annex \ref{annex:probabilistic}} +\paragraph{Distribution of $ T_i $} We first studied how many items were +present per bin. + +\paragraph{Distribution of $ V_i $} We then looked at the size of the first +item in each bin. + +\paragraph{Asymptotic behavior of $ H_n $} Finally, we analyzed how many bins +were needed to store $ n $ items. + +% TODO histograms +% TODO analysis histograms