\subsection{Results timing kbemis}
\label{sec:results-timing-kbemis}

First timing experiment:

New data was generated for each run, so that caching should not have an effect on the timing results. There is no clear pattern in the first series of timing results, with wide variability fof the "M + R/W" results. Unfortunately, the earlier runs show outliers due to the influence of other users running jobs at the same time. 

Second timing experiment:

Again, new data was generated for each run. There appears to be a U-shaped curve in the timing results for M + R/W, with decreasing time as subset size increases, until it hits the minimum at a sweet spot of ~$2^12$ subsets, and the timings begin to increase again.

Third timing experiment:

I was able to run at most $2^28$ rows before the server ran out of space and jobs began failing. For $2^28$ rows, glmfit took a little under 7 minutes.

Fourth timing experiment:

Again the same protocol was followed. After little increase in time for smaller numbers of rows, the total log time for glmfit begins to increase linearly with every increase in the log number of rows.

\begin{figure}
  \centering
  \includegraphics[height = 6.5in, width= 5in, angle = -90]{kbemis.timing.plot.1.ps}
  \caption{Results of the first timing experiment (kbemis)}
  \label{fig:kbemis}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[height = 6.5in, width= 5in, angle = -90]{kbemis.timing.plot.2.ps}
  \caption{Results of the second timing experiment (kbemis)}
  \label{fig:kbemis}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[height = 6.5in, width= 5in, angle = -90]{kbemis.timing.plot.4.ps}
  \caption{Results of the fouth timing experiment (kbemis)}
  \label{fig:kbemis}
\end{figure}
