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 solve this problem for arbitrary access patterns by randomly mapping blocks of a logical address space to the disks.We show that a shared buffer of O(D) blocks suffices to support efficient writing. The analysis uses the properties of negative association to handle dependencies between the random variables involved. This approach might be of independent interest for probabilistic analysis in general.If two randomly allocated copies of each block exist, N arbitrary blocks can be read within 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 without a big impact on reading efficiency. From the point of view of external memory models, these results rehabilitate Aggarwal and Vitter's "single-disk multi-head" model [1] 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 [2] 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.

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