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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 We implemented the NFBP algorithm in Python \footnotemark, for its ease of use
and broad recommendation. We used the \texttt{random} library to generate and broad recommendation. We used the \texttt{random} library to generate
random numbers between $ 0 $ and $ 1 $ and \texttt{matplotlib} to plot the 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}} \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