MPI-I-1999-1-003

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.