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When multiple jobs compete for processing resources on a parallel computer, the operating system kernel's processor allocation policy determines how many and which processors to allocate to each. In this paper we investigate the issues involved in constructing a processor allocation policy for large scale, message-passing parallel computers supporting a scientific workload.We make four specific contributions:We define the concept of efficiency preservation as a characteristic of processor allocation policies. Efficiency preservation is the degree to which the decisions of the processor allocator degrade the processor efficiencies experienced by individual applications relative to their efficiencies when run alone. We identify the interplay between the kernel processor allocation policy and the application load distribution policy as a determinant of efficiency preservation. We specify the details of two families of processor allocation policies, called Equipartition and Folding. Within each family, different member policies cover a range of efficiency preservation values, from very high to very low.By comparing policies within each family as well as between families, we show that high efficiency preservation is essential to good performance, and that efficiency preservation is a more dominant factor in obtaining good performance than is equality of resource allocation.