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tex: NFBP distribution boilerplate

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Paul ALNET 2023-06-04 11:41:47 +02:00
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@ -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