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Abstract:
High performance applications involving large data sets require the
efficient and flexible use of multiple disks. In an external memory
machine with D parallel, independent disks, only one block can be
accessed on each disk in one I/O step. This restriction leads to a
load balancing problem that is perhaps the main inhibitor for the
efficient adaptation of single-disk external memory algorithms to
multiple disks. We show how this problem can be solved efficiently by
using randomization and redundancy. A buffer of O(D) blocks suffices
to support efficient writing of arbitrary blocks if blocks are
distributed uniformly at random to the disks (e.g., by hashing). If
two randomly allocated copies of each block exist, N arbitrary blocks
can be read within ceiling(N/D)+1 I/O steps with high probability.
The redundancy can be further reduced from 2 to 1+1/r for any integer
r. From the point of view of external memory models, these results
rehabilitate Aggarwal and Vitter's "single-disk multi-head" model that
allows access to D arbitrary blocks in each I/O step. This powerful
model can be emulated on the physically more realistic independent
disk model with small constant overhead factors. Parallel disk
external memory algorithms can therefore be developed in the
multi-head model first. The emulation result can then be applied
directly or further refinements can be added.
