implemented algorithm

Socksorting/project.tex

@@ -73,7 +73,7 @@ algorithm from the paper by \citeauthor{My colleague et al.} Which is the curren
 industry standard. Notice the code has a runtime complexity of $\mathcal{O}(n^2)$.
 
 \begin{algorithm}
-  \caption{Conventional sock sorting}\label{euclid}
+  \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
@@ -121,7 +121,36 @@ obsolete.
 \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:
 
 
 \section{Conclusion}