Abstract
The time complexity of searching a sorted list ofn elements in parallel on a coarse grained network of diameterD and consisting ofN processors (wheren may be much larger thanN) is studied. The worst case period and latency of a sequence of pipeline search operation are easity seen to be Ω(logn−logN) and Ω(D+logn−logN), respectively. Since forn=N 1+Ω(1) the worst-case period is Ω(logn) (which can be achieved by a single processor), coarse-grained networks appear to be unsuitable for the search problem. By contrast, it is demonstrated using standard queuing theory techniques that a constant expected period can be achieved provided thatn=O(N2 N).
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This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grants A3336 and A9173.
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Akl, S.G., Dehne, F. Pipelined search on coarse grained networks. Int J Parallel Prog 18, 359–364 (1989). https://doi.org/10.1007/BF01379185
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DOI: https://doi.org/10.1007/BF01379185