tex: add NFB(D)P drawings

latex/content.tex

@@ -110,6 +110,42 @@ Our goal is to study the number of bins $ H_n $ required to store $ n $ items
 for each algorithm. We first consider the Next Fit Bin Packing algorithm, where
 we store each item in the next bin if it fits, otherwise we open a new bin.
 
+\begin{figure}[h]
+	\centering
+	\begin{tikzpicture}[scale=0.8]
+		% Bins
+		\draw[thick] (0,0) rectangle (2,6);
+		\draw[thick] (3,0) rectangle (5,6);
+		\draw[thick] (6,0) rectangle (8,6);
+
+		% Items
+		\draw[fill=red] (0.5,0.5) rectangle (1.5,3.25);
+		\draw[fill=blue] (0.5,3.5) rectangle (1.5,5.5);
+		\draw[fill=green] (3.5,0.5) rectangle (4.5,1.5);
+		\draw[fill=orange] (3.5,1.75) rectangle (4.5,3.75);
+		\draw[fill=purple] (6.5,0.5) rectangle (7.5,2.75);
+		\draw[fill=yellow] (6.5,3) rectangle (7.5,4);
+
+		% arrow
+		\draw[->, thick] (8.6,3.5) -- (7.0,3.5);
+		\draw[->, thick] (8.6,1.725) -- (7.0,1.725);
+
+		% Labels
+		\node at (1,-0.75) {Bin 0};
+		\node at (4,-0.75) {Bin 1};
+		\node at (7,-0.75) {Bin 2};
+		\node at (10.0,3.5) {Yellow item};
+		\node at (10.0,1.725) {Purple item};
+
+	\end{tikzpicture}
+	\label{fig:nfbp}
+	\caption{Next Fit Bin Packing example}
+\end{figure}
+
+\paragraph{} The example in figure \ref{fig:nfbp} shows the limitations of the
+NFBP algorithm. The yellow item is stored in bin 2, while it could fit in bin
+1, because the purple item is considered first and is too large to fit.
+
 \paragraph{} Each bin will have a fixed capacity of $ 1 $ and items and items
 will be of random sizes between $ 0 $ and $ 1 $. We will run X simulations % TODO
 with 10 packets.
@@ -170,7 +206,41 @@ were needed to store $ n $ items.
 
 \section{Next Fit Dual Bin Packing algorithm}
 
-The variables used are the same as for NFBP.
+Next Fit Dual Bin Packing is a variation of NFBP in which we allow the bins to
+overflow. A bin must be fully filled, unless it is the last bin.
+
+\begin{figure}[h]
+	\centering
+	\begin{tikzpicture}[scale=0.8]
+		% Bins
+		\draw[thick] (0,0) rectangle (2,6);
+		\draw[thick] (3,0) rectangle (5,6);
+
+		% Transparent Tops
+		\fill[white,opacity=1.0] (0,5.9) rectangle (2,6.5);
+		\fill[white,opacity=1.0] (3,5.9) rectangle (5,6.5);
+
+		% Items
+		\draw[fill=red] (0.5,0.5) rectangle (1.5,3.25);
+		\draw[fill=blue] (0.5,3.5) rectangle (1.5,5.5);
+		\draw[fill=green] (0.5,5.75) rectangle (1.5,6.75);
+		\draw[fill=orange] (3.5,0.5) rectangle (4.5,2.5);
+		\draw[fill=purple] (3.5,2.75) rectangle (4.5,5.0);
+		\draw[fill=yellow] (3.5,5.25) rectangle (4.5,6.25);
+
+		% Labels
+		\node at (1,-0.75) {Bin 0};
+		\node at (4,-0.75) {Bin 1};
+
+	\end{tikzpicture}
+	\caption{Next Fit Dual Bin Packing example}
+	\label{fig:nfdbp}
+\end{figure}
+
+\paragraph{} The example in figure \ref{fig:nfdbp} shows how NFDBP utilizes
+less bins than NFBP, due to less stringent constraints. The top of the bin is
+effectively removed, allowing for an extra item to be stored in the bin. We can
+easily see how with NFDBP each bin can at least contain two items.
 
 \subsection{La giga demo}
 

latex/main.tex

@@ -14,6 +14,7 @@
 \usepackage[english]{babel}
 \usepackage{eso-pic} % for background on cover
 \usepackage{listings}
+\usepackage{tikz}
 
 % Define colors for code
 \definecolor{codegreen}{rgb}{0,0.4,0}