diff --git a/Culinography/Licking Rocks .pdf b/Culinography/Licking Rocks .pdf new file mode 100644 index 0000000..2d047e2 Binary files /dev/null and b/Culinography/Licking Rocks .pdf differ diff --git a/Culinography/img/ancient_egyptians.png b/Culinography/img/ancient_egyptians.png index 3c838a7..a6f6a65 100644 Binary files a/Culinography/img/ancient_egyptians.png and b/Culinography/img/ancient_egyptians.png differ diff --git a/Socksorting/bibliography.bib b/Socksorting/bibliography.bib index 81e80bd..e69de29 100644 --- a/Socksorting/bibliography.bib +++ b/Socksorting/bibliography.bib @@ -1,7 +0,0 @@ -@article{otherarticle, - title = {A first approach to sock sorting}, - journal = {Journal of laundry science}, - author = {My colleague et al.}, - year = {1969}, - month = {13} -} diff --git a/Socksorting/defs.tex b/Socksorting/defs.tex index e73e66e..e69de29 100644 --- a/Socksorting/defs.tex +++ b/Socksorting/defs.tex @@ -1,286 +0,0 @@ -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - 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-\input{defs.tex} -\input{mydefs.tex} - -\addbibresource{bibliography.bib} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{document} - -\fancyhf{} -\pagestyle{fancy} -\lhead{} -\rhead{CelloClemens et al.} -\cfoot{\thepage } - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\clearpage - -% PROJECTS -\newcommand{\projectpath}{} % Necessary because of the inclusion of extra files -\begin{refsection} -\include{project} -\end{refsection} -\end{document} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - diff --git a/Socksorting/mydefs.tex b/Socksorting/mydefs.tex index 01f1439..e69de29 100644 --- a/Socksorting/mydefs.tex +++ b/Socksorting/mydefs.tex @@ -1,14 +0,0 @@ -\usepackage{lipsum} -\usepackage[T1]{fontenc} -\usepackage[sfdefault]{biolinum} -\biolinum -\usepackage{listings} -\usepackage{mathrsfs} -\usepackage{algorithm} -\usepackage{algorithmicx} -\usepackage{algpseudocode} -\usepackage{emoji} -\usepackage{soul} - - -\newcommand{\acronym}{HADES } \ No newline at end of file diff --git a/Socksorting/project.tex b/Socksorting/project.tex index 02cc1d1..e69de29 100644 --- a/Socksorting/project.tex +++ b/Socksorting/project.tex @@ -1,201 +0,0 @@ -\twocolumn[ - \title{\bf \acronym (High end, Advanced, Data driven, Enterprise grade Sock sorting algorithm) - An algorithm for faster sock sorting} - \author{ - CelloClemens$^{1,2}$, - Henri\emoji{duck}$^{1}$, - } - \date{\today} - % List of institutions - \maketitle - $^{1}$Department for theoretical laundry science, Karlsruhe institute of suffering and sorrow (KISS), Karlsruhe, Germany \\ - $^{2}$Institute of laundry sorting, Department for socks, Karlsruhe institute of suffering and sorrow (KISS), Karlsruhe, Germany - \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 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} -] -\fancypagestyle{firstpage}{% - \lhead{Please help I am stuck in the basement sorting socks} - \rhead{Journal of Immaterial Science} -} -\thispagestyle{firstpage} - -% The introduction -\section{Introduction} -While sorting algorithms are one of the most discussed algorithms in the -computer science community, application of this field to laundry is still quite new. -In fact no research is known to the authors connecting the fields of computer science -and laundry sorting. A few definitions are required in order to establish a baseline -for the algorithm discussed in the following paper. - -\subsection{Definitions} -In this section a few definitions, common in the field of theoretical laundry science shall be -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 -search for this isomorphism $\eta$ and matching every sock $s$ to its inverse -$s^{-1}$. -\begin{figure}[h] - \centering - \includegraphics[width=\columnwidth]{\projectpath figs/Sock.jpeg} - \vspace{0.1in} - \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 -triplet $(\Lambda, +, -)$ representing a datastructure that implements -the following functions: -\begin{itemize} - \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 my colleague which is the current -industry standard. Notice the code has a runtime complexity of $\mathcal{O}(n^2)$. - -\begin{algorithm} - \caption{Conventional sock sorting} - \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{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{0.2in} -\end{figure} - -\section{Algorithm} -Making use of the novel advanced features of a "drying rack" we are able to -implement the following algorithm in $\mathscr{O}(n)$:\\ -\begin{algorithm} - \caption{\acronym} - \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 $\text{matches}\gets []$ - \State $\daleth\gets []$ \Comment{Create a new empty drying rack} - \Repeat - \State $\mathscr{L}\gets $ A.get - \State result $\gets$ $\daleth$.match($\mathscr{L}$) - \If{result $\ne\mathscr{L}_0$} - \State matches.append(result) - \Else - \State $\daleth$.put($\mathscr{L}$) - \EndIf - - \Until{$\mathscr{L}\ne\mathscr{L}_0$} - \end{algorithmic} -\end{algorithm} -As evident from the algorithm above, only one loop performing -operations which are all in $\mathscr{O}(1)$ is required thus -putting the algorithm in a $\mathscr{O}(n)$ runtime complexity -class. Assuming that $\forall\mathscr{L}\in\Lambda\exists\mathscr{L}^{-1}|\mathscr{L}\cong\mathscr{L}^{-1}$ -the algorithm always yields a correct solution for the problem -(proof is left as an exercise to the reader). -\section{Discussion and Results} -To evaluate the algorithms performance it has been executed -on different platforms consisting of diverse hardware:\\ -\resizebox*{\linewidth}{!}{ - \begin{tabular}[]{l||l|c} - \textbf{Hardware} & \textbf{Algorithm} & \textbf{Runtime [s]} \\ - \hline - Myself & Conventional (n=20) & 352.7 \\ - Myself & \acronym (n=20) & 92.3 \\ - Myself & Conventional (n=100) & 42069 \\ - Myself & \acronym (n=100) & 420.69 \\ - \hline - My roommate & Conventional (n=10) & 91.7 \\ - My roommate & \acronym (n=10) & -2 \\ - \hline - Girlfriend & n.a. & n.a. - \end{tabular} -}\\ -\begin{figure}[h] - \begin{center} - \includegraphics[width=\linewidth]{figs/graph.png} - \bigskip - \caption{Comparative statistical time analysis of both algorithms. - The graph depicts algorithm runtime (y-axis) and graphs it against - input size (x-axis). Data for - \acronym in blue, for conventional sock sorting in green.} - \end{center} -\end{figure}\\ -From the above data it is evident that \acronym bears a clear advantage in comparison -to the conventional algorithm when it comes to sock sorting. Utilizing advanced statistical modelling we calculated a -speedup factor of about $3.1415926535897932384626433\cdot n$. The data also illustrates -the scalability of the algorithm and its adaptability to different hardware. -\section{Conclusion} -It can be concluded that the algorithm presented in this paper is -greatly superior to the conventional method of sorting socks. -It will probably revolutionize not only the field of laundry science but -also have great impact in the industry.\\ -The datastructures outlined above may become abundantly used and be the future -industry standard. Although the field of laundry science is still rather new -there are still a lot of open questions to be answered. However it is unlikely -that a faster sock sorting algorithm than \acronym can be developed. -\section{Acknowledgements} -We shall use this historic opportunity to thank the Journal of immaterial science -for publishing great \st{memes} research. We also want to thank our university -for giving us this great opportunity for \st{depression and self loathing} -research and personal advancement.\\ -It is also only appropriate to thank the air. Without it no laundry would be -dry and we would not have written this paper.\\ - - -\printbibliography[] diff --git a/build/Culinography.pdf b/build/Culinography.pdf index 733c0d1..e69de29 100644 Binary files a/build/Culinography.pdf and b/build/Culinography.pdf differ diff --git a/build/Socksorting.pdf b/build/Socksorting.pdf index 9ed4fab..e69de29 100644 Binary files a/build/Socksorting.pdf and b/build/Socksorting.pdf differ