ALCOMFT-TR-01-79

David A. Hutchinson, Peter Sanders and Jeffrey S. Vitter
Duality between prefetching and queued writing with Parallel Disks
MPI. Work packages 1 and 4. May 2001.

Abstract: 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 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 the integrated caching and prefetching problem, in which blocks can be accessed multiple times. Another application of duality gives us the first external sorting sorting algorithms that are provably optimal in an asymptotic sense, in which we take into consideration the constant factors. One of these algorithms is a simple and practical variant of multiway merge sort, addressing a question that has been open for some time.

Postscript file: ALCOMFT-TR-01-79.ps.gz (103 kb).