whats a laundry rack?

mydefs.tex

@@ -7,6 +7,7 @@
 \usepackage{algorithm}
 \usepackage{algorithmicx}
 \usepackage{algpseudocode}
+\usepackage{emoji}
 
 
-\newcommand{\acronym}{<stupid acronym>}
+\newcommand{\acronym}{HADES }

project.tex

@@ -1,8 +1,8 @@
 \twocolumn[
-  \title{\bf \acronym - An algorithm for faster sock sorting}
+  \title{\bf \acronym (High end, Advanced, Data driven, Enterprise grade Sock sorting algorithm) - An algorithm for faster sock sorting}
   \author{
     CelloClemens$^{1,2}$,
-    Henriente$^{1}$,
+    Henri\emoji{duck}$^{1}$,
   }
   \date{\today}
   % List of institutions
@@ -12,7 +12,7 @@
   \begin{psummary}
     Sorting socks can often be a time consuming task. This paper introduces the fastest method known in the scientific community to tackle
     this challanging task. To be able to implement this new algorithm
-    a new data structure will be introduced and discussed. Abundant application of this novel algorithm may be able to
+    a new datastructure will be introduced and discussed. Abundant application of this novel algorithm may be able to
     reduce the time required for sorting socks considerably.
   \end{psummary}
   \vspace{2mm}
@@ -46,13 +46,13 @@ $s^{-1}$.
   \centering
   \includegraphics[width=\columnwidth]{\projectpath figs/Sock.jpeg}
   \vspace{0.1in}
-  \caption{Three single socks.}
+  \caption{A pair of blue socks and a single orange sock.}
   \label{fig:Sock}
   \vspace{0.1in}
 \end{figure}
 \subsubsection{Laundry basket}
 Let $\Lambda\subseteq\Lambda_a$ be a set of laundry items. Then a laundry basket is a
-triple $(\Lambda, +, -)$ representing a data structure that implements
+triplet $(\Lambda, +, -)$ representing a datastructure that implements
 the following functions:
 \begin{itemize}
   \item \texttt{get: }$\mathscr{L}\in\Lambda_a$, returns a uniformly random
@@ -70,7 +70,7 @@ To fully appreciate the gravity of \acronym it has to first be discussed
 how most resent research tackles the problem of sock sorting.
 The following code describes the most recently developed sock sorting
 algorithm from the paper by \citeauthor{My colleague et al.} Which is the current
-industry standard. Notice whe code has a runtime complexity of $\mathcal{O}(n^2)$.
+industry standard. Notice the code has a runtime complexity of $\mathcal{O}(n^2)$.
 
 \begin{algorithm}
   \caption{Conventional sock sorting}\label{euclid}
@@ -88,8 +88,39 @@ industry standard. Notice whe code has a runtime complexity of $\mathcal{O}(n^2)
     \Until{$\mathscr{L}\ne\mathscr{L}_0$}
   \end{algorithmic}
 \end{algorithm}
-\section{Methodology}
 
+\section{Concepts}
+The basis for every fast algorithm are  simple yet equally fast
+datastructures. To enable the low runtime achieved by \acronym,
+the introduction of a new datastructure, the "laundry rack" is integral.
+
+\subsection{Laundry rack}
+Let $\Lambda\subseteq\Lambda_a$ be a set of laundry. A laundry rack (See figure \ref{fig:Rack}) is a
+triplet $(\Lambda, +, -)$ representing a datastructure that implements the
+following methods:
+\begin{itemize}
+  \item \texttt{get($\mathscr{L}\in\Lambda$)}: $\mathscr{L}\in\Lambda$, gets
+        a specific laundry item from the laundry rack.
+  \item \texttt{put($\mathscr{L}\in\Lambda$)}, deposits a laundry item onto
+        the laundry rack.
+  \item \texttt{match($\mathscr{L}\in\Lambda$)}: $(\mathscr{P}\in\Lambda\times\Lambda)|\mathscr{L}_0$,
+        returns a tuple $(\mathscr{L}, \mathscr{L}^{-1})$ representing
+        a pair of socks iff $\mathscr{L}^{-1}$ is already on the laundry rack,
+        $\mathscr{L}_0$ otherwise.
+\end{itemize}
+All these operations (especially \texttt{match}) run in $\mathcal{O}(1)$,
+making iteration over all $n$ laundry items to find a pair $(\mathscr{L}, \mathscr{L}^{-1})$
+obsolete.
+\begin{figure}[h]
+  \centering
+  \includegraphics[width=\columnwidth]{\projectpath figs/rack.jpeg}
+  \vspace{0.1in}
+  \caption{A blue drying rack, found in many housholds.}
+  \label{fig:Rack}
+  \vspace{0.1in}
+\end{figure}
+
+\section{Algorithm}
 \section{Discussion and Results}
 
 
@@ -97,8 +128,6 @@ industry standard. Notice whe code has a runtime complexity of $\mathcal{O}(n^2)
 
 \section{Acknowledgements}
 
-I did this all by myself, so I'm kinda awesome. But I guess I hocked and edited this template from the cowshed article so thanks for that William Roper
-
 \begingroup
 \setlength\bibitemsep{0pt}
 \setlength\bibnamesep{0pt}