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We propose a taxonomy of parallel sorting that encompasses a broad range of array-and file-sorting algorithms. We analyze how research on parallel sorting has evolved, from the earliest sorting networks to shared memory algorithms and VLSI sorters. In the context of sorting networks, we describe two fundamental parallel merging schemes: the odd-even and the bitonic merge. We discuss sorting algorithms that evolved from these merging schemes for parallel computers, whose processors communicate<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2514.2516">doi:10.1145/2514.2516</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dc2bhjocynep5mfp3ntak3cfrq">fatcat:dc2bhjocynep5mfp3ntak3cfrq</a> </span>
more »... rough interconnection networks such as the perfect shuffle, the mesh, and a number of other sparse networks. Following our discussion of network sorting algorithms, we describe how faster algorithms have been derived from parallel enumeration sorting schemes, where, with a shared memory model of parallel computation, keys are first ranked and then rearranged according to their rank. Parallel sorting algorithms are evaluated according to several criteria related to both the time complexity of an algorithm and its feasibility from the viewpoint of computer architecture. We show that, in addition to attractive communication schemes, network sorting algorithms have nonadaptive schedules that make them suitable for implementation. In particular, they are easily generalized to block sorting algorithms, which utilize limited parallelism to solve large sorting problems. We also address the problem of sorting large mass-storage files in parallel, using modified disk devices or intelligent bubble memory. We conclude by mentioning VLSI sorting as an active and promising direction for research on parallel sorting.
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