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project.tex
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\twocolumn[
\title{\bf <Stupid acronym> - An algorithm for faster sock sorting}
\title{\bf \acronym - An algorithm for faster sock sorting}
\author{
CelloClemens$^{1,2}$,
Henriente$^{1}$,
@ -37,9 +37,9 @@ introduced. These are required to understand the algorithm and its advantages.
\subsubsection{Sock}
Let $\Lambda_a$ be the Set of laundry. The set of socks, $\Sigma\subset\Lambda_a$
is defined as $\Sigma:=\{s\in\Lambda_a|\chi(s)=1\}$\footnote{Yes, some socks have holes. So what?!}, where $\chi(s)$ is the Euler
characteristic of $s$. For every sock $s$ there is an equal counterpart $s^{-1}$ giving rise
to the identity $s\cong s^{-1}$. The task commonly known as "sock sorting" is in fact the
is defined as $\Sigma:=\{s\in\Lambda_a|\chi(s)=1\}$\footnote{Yes, some socks have holes. So what?!}, where $\chi(s)$ is the Euler
characteristic of $s$. For every sock $s$ there is an equal counterpart $s^{-1}$ giving rise
to the identity $s\cong s^{-1}$. The task commonly known as "sock sorting" is in fact the
search for this isomorphism $\eta$ and matching every sock $s$ to its inverse
$s^{-1}$.
\begin{figure}[h]
@ -51,67 +51,50 @@ $s^{-1}$.
\vspace{0.1in}
\end{figure}
\subsubsection{Laundry basket}
Let $\Lambda$ be a set of laundry items. Then a laundry basket is a
triple $(\Lambda, +, -)$ representing a data structure that implements
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
the following functions:
\begin{itemize}
\item \lstinline{}
\item \texttt{get: }$\mathscr{L}\in\Lambda_a$, returns a uniformly random
laundry item from the basket or $\mathscr{L}_0$, the Zero element of laundry, iff
There are no items left.
\item \texttt{put($\mathscr{L}\in\Lambda_a$)}, deposits the given laundry item
into the basket.
\end{itemize}
Note that both operations run in $\mathcal{O}(1)$. Because of the nature of
a laundry basket finding a unique item requires transferring the content of
the whole basket to a new basket thus requiring $\mathcal{O}(n)$ operations,
$n$ being the number of items currently inside the basket.
\subsection{Ongoing and latest research}
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 $\mathcal{O}(n^2)$.
\begin{algorithm}
\caption{Conventional sock sorting}\label{euclid}
\begin{algorithmic}[1]
\State\Comment initialize a new laundry basket with a given set of laundry
\State $A\gets\Lambda$\Comment WLOG assume $\forall\mathscr{L}\in\Lambda|\mathscr{L}$ is a sock
\State $\text{matches}\gets []$
\Repeat
\State $\mathscr{L}\gets$ A.get
\Repeat\Comment find the inverse Sock by checking all other socks
\State $\mathscr{L}^\prime\gets$ A.get
\Until{$\mathscr{L}^\prime =\mathscr{L}^{-1}$}
\State matches.append(($\mathscr{L}, \mathscr{L}^\prime$))
\Until{$\mathscr{L}\ne\mathscr{L}_0$}
\end{algorithmic}
\end{algorithm}
\section{Methodology}
In order to invent this thing or analyze this data, we're going to need to use the equation below.
\begin{equation}
Heuristic_\alpha(x) = \sqrt{\sum{All of the things}},
\end{equation}
Of course we trust that equation because of the work done in \cite{OnlineRef1} which may or may not agree with the dude that wrote \cite{ArticleRef}.
\section{Another Section}
I don't know, you could have a boring data collection bit here, or an architecture, or something. I'm sure it'll be mostly filler.
\section{Filler Section 2}
As shown in figure , Freud is not displaying Penis envy by holding a cigar.
I swear it's just a cigar.
\section{Discussion and Results}
According to all of this data and our unbiased analysis, all of our beliefs have been validated. Just check out Table \ref{table:1}.
\begin{table}[h!]
\vspace{0.1in}
\begin{center}
\begin{tabular}{||c c c c||}
\hline
Col1 & Col2 & Col2 & Col3 \\ [0.5ex]
\hline\hline
1 & 6 & 87837 & 787 \\
\hline
2 & 7 & 78 & 5415 \\
\hline
3 & 545 & 778 & 7507 \\
\hline
4 & 545 & 18744 & 7560 \\
\hline
5 & 88 & 788 & 6344 \\ [1ex]
\hline
\end{tabular}
\vspace{0.1in}
\caption{Table to prove how right you are.}
\label{table:1}
\end{center}
\end{table}
Wow, what astounding results!
\section{Conclusion}
In conclusion, I am very smart
\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
@ -121,6 +104,3 @@ I did this all by myself, so I'm kinda awesome. But I guess I hocked and edited
\setlength\bibnamesep{0pt}
\printbibliography[heading=subbibliography]
\endgroup
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