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Cylinder Remapping
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Vongsathorn and Carson: arrange disk cylinders to ``match'' request stream\\
\quad\\
specifically:\\
\quad $N$ cylinders\\
\quad $\pi_i$ prob. read/write head on cylinder $i$\\
\quad $\rho_{i,j}$ prob. next cylinder is $j$, given head is on $i$

Minimize expected seek distance: find\\ 
permutation, $P$, of \{1,2,...,$N$\} that minimizes
$$
E[P] =  \sum_{i=1}^N \sum_{j=1}^N |P(i) - P(j)| \pi_i \rho_{ij}
$$
and then remap according to $P$.  

oops: \\
number of permutations is $N$! where $N \approx 2000$;
2000! $\approx 10^{5736}$ $\Rightarrow$ intractable problem (?)
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