Bounds on the separation of two parallel disk models

The single-disk, D-head model of parallel I/0 was introduced by Agarwal and Vitter to analyze algorithms for problem instances that are too large to fit in primary memory. Subsequently Vitter and Shriver proposed a more realistic model in which the disk space is partitioned into D disks, with a single head per disk. To date, each problem for which there is a known optimal algorithm for both models has the same asymptotic bounds on both models. Therefore, it has been unknown whether the models are equivalent or whether the singledisk model is strictly more powerful. In this pape:r we provide evidence that the single-disk model is strictly more powerful. We prove a lower bound on any general simulation of the single-disk model on the multi-disk model and establish randomized and deterministic upper bounds. Let N be the problem size and let T be the number of parallel I/Os required by a program on the single-disk model. Then any simulation of this pro€:ram on the multi-disk model will require Q ( T 10~/:,C:Ct~b:~) parallel I/Os. This lower bound holds even if replication is allowed in the multi-disk model. *Department of Computer Science, University of Hartford, 200 Bloomfield Avenue, W. Hartford, CT 06117-1599. Email: armenGhartford.edu. This work was done while the author was a graduate student at Dartmouth College. Permission 10 make digital/hard copies of all or part of this material for personal or classroom use its granted without fee provided that the copies a.re not made or distributed for profit or commercial advantage, the copynght notice, the title of the publication and its date appear, and notice is given that copyright is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires specific permission and/or fee. 10PADS'96, Philadelphia PA, USA o 1996 ACM 0-89791-813-4/96/05 .. $3.50 122 We also show an 0 Co~0f0~ D) randomized upper bound and an 0 (log D(log log D) ) deterministic upper bound. These results exploit an interesting analogy between the disk models and the PRAM and DCM models of parallel computation.