\begin{slide}{violet}
\violet
Vongsathorn and Carson: approximate!
\quad\\
\begin{itemize}
\item assume independent access, $\rho_{i,j} = \pi_j$, 
\item find $P$ to minimize
$$
E[P] =  \sum_{i=1}^N \sum_{j=1}^N |P(i) - P(j)| \pi_i \pi_{j}
$$
\item (Knuth vol. 3) minimizing $P$ is {\it pipe organ}
\end{itemize}
DG counterpoint: access is independent NOT!! \\
e.g. file index node (inode) access $\rightarrow$ access the data blocks of that file\\
\quad\\
design: Disk Allocation Regions (DAR)s

\pagebreak[4]

Examine this issue:
\begin{enumerate}
\item Do we have real data from our system that allows us to
reject the independence assumption in favor of a specific Markov model?
\item Does 1 matter, i.e., even if the answer is yes, can we improve
significantly upon the pipe organ arrangement?
\end{enumerate}
\end{slide}

