Duality Between Prefetching and Queued Writing with Parallel Disks

This is the published version, made available with the permission of the publisher. Copyright © 2005 Society for Industrial and Applied Mathematics.Parallel disks promise to be a cost effective means for achieving high bandwidth in applications involving massive data sets, but algorithms for parallel disks can be difficult to devise. To combat this problem, we define a useful and natural duality between writing to parallel disks and the seemingly more difficult problem of prefetching. We first explore this duality for applications involving read-once accesses using parallel disks. We get a simple linear time algorithm for computing optimal prefetch schedules and analyze the efficiency of the resulting schedules for randomly placed data and for arbitrary interleaved accesses to striped sequences. Duality also provides an optimal schedule for prefetching plus caching, where blocks can be accessed multiple times. Another application of this duality gives us the first parallel disk sorting algorithms that are provably optimal up to lower-order terms. One of these algorithms is a simple and practical variant of multiway mergesort, addressing a question that had been open for some time