A taxonomy of parallel sorting

In this paper, we propose a taxonomy of parallel sorting that includes a broad range of array and file sorting algorithms. We analyze the evolution of research on parallel sorting, from the earliest sorting networks to the shared memory algorithms and the VLSI sorters. In the context of sorting networks, we describe two fundamental parallel merging schemes the odd-even and the bitonic merge. Sorting algorithms have been derived from these merging algorithms for parallel computers where processors communicate through interconnection networks such as the perfect shuffle, the mesh and a number of other sparse networks. After describing the network sorting algorithms, we show that, with a shared memory model of parallel computation, faster algorithms have been derived from parallel enumeration sorting schemes, where keys are first ranked and then rearranged according to their rank. Parallel sorting algorithms are evaluated according to a number of criteria, related not only to their time complexity, but also to their feasibility from a computer architecture point of view. We show that in addition to their attractive communication schemes, network sorting algorithms have non-adaptive schedules that make them suitable for implementation. In particular, they are easily generalized to block-sorting algorithms, that 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 memories. Finally, the newer area of VLSI sorting is mentioned as an active and promising direction of research on parallel sorting.