Parallel Sorting with Minimal Data

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For reasons of efficiency, parallel methods are normally used to work with as many elements as possible. Contrary to this preferred situation, some applications need the opposite. This paper presents three parallel sorting algorithms suited for the extreme case where every process contributes only a single element. Scalable solutions for this case are needed for the communicator constructor MPI_Comm_split. Compared to previous approaches requiring O(p) memory, we introduce two new parallel sorting algorithms working with a minimum of O(1) memory. One method is simple to implement and achieves a running time of O(p). Our scalable algorithm solves this sorting problem in O(log2 p) time.