Parallel-sorting algorithms for hypercube multiprocessors
Thesis/Dissertation
·
OSTI ID:6155985
Four different parallel sorting algorithms for hypercube connected distributed memory multiprocessors are presented. The algorithms balance the loads of the hypercube nodes by deterministic selection of the exact partitioning keys. The first algorithm presented has a time complexity of O(n/p log n + p{sup 2}log{sup 2} n), where n is the number of elements being sorted, p = 2{sup d} is the number of processors, and d is the dimension of the hypercube. The second algorithm approximates the former with a time complexity of O(n/p log n + p{sup 2} log n). Generalization of the first algorithm uses one of the topological properties of the hypercube graph for partitioning, and gives a class of sorting algorithms with a time complexity of O(n/p log n + p{sup 1+1/k}log{sup 1+k}n), where k is an arbitrary positive integer 0 < k < d. The fourth algorithm, with an expected time complexity of O(n/p log n + p log{sup 2} n), is suitable for large hypercubes. All algorithms route elements directly to their destination nodes by means of the distance-d communication capability of recently introduced hypercube systems and novel conflict-free routing algorithms. Interprocessor communication is also overlapped with the computation to further increase the efficiency. Experimental results on a 16 node 386-based iPSC/2 hypercube system are presented, and speedups for up to 2,048 node hypercubes are estimated. The problem of dynamic subcube allocation in a multiuser hypercube multiprocessor is also addressed. The dynamic allocation model takes into account the subcubes released by users which can cause fragmentation of the hypercube. Algorithms are presented for showing the existence of a free subcube (candidate) of the requested dimension, for finding the addresses of the candidates, and for choosing a subcube from the set of candidate subcubes which will ultimately result in less fragmentation of the hypercube.
- Research Organization:
- Ohio State Univ., Columbus, OH (USA)
- OSTI ID:
- 6155985
- Country of Publication:
- United States
- Language:
- English
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