Minimizing stall time in single and parallel disk systems

We study integrated prefetching and caching problems following the work of Cao et. al. and Kimbrel and Karlin. Cao et. al. and Kimbrel and Karlin gave approximation algorithms for minimizing the total elapsed time in single and parallel disk settings. The total elapsed time is the sum of the processor stall times and the length of the request sequence to be served. We show that an optimum prefetching/caching schedule for a single disk problem can be computed in polynomial time, thereby settling an open question by Kimbrel and Karlin. For the parallel disk problem we give an approximation algorithm for minimizing stall time. Stall time is an important and harder to approximate measure for this problem. All of our algorithms are based on a new approach which involves formulating the prefetching/caching problems as integer programs.