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Approximate and exact deterministic parallel selection

  • Shiva Chaudhuri
  • Torben Hagerup
  • Rajeev Raman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)

Abstract

The selection problem of size n is, given a set of n elements drawn from an ordered universe and an integer r with 1<rn, to identify the rth smallest element in the set. We study approximate and exact selection on deterministic concurrent-read concurrent-write parallel RAMs, where approximate selection with relative accuracy λ>0 asks for any element whose true rank differs from r by at most An. Our main results are: (1) For all t≥(log log n)4, approximate selection problems of size n can be solved in O(t) time with optimal speedup with relative accuracy \(2^{{{ - t} \mathord{\left/{\vphantom {{ - t} {\left( {\log \log n} \right)}}} \right.\kern-\nulldelimiterspace} {\left( {\log \log n} \right)}}^4 }\); no deterministic PRAM algorithm for approximate selection with a running time below Ο(log n/log log n) was previously known. (2) Exact selection problems of size n can be solved in O(log n/log log n) time with O(n log log n/log n) processors. This running time is the best possible (using only a polynomial number of processors), and the number of processors is optimal for the given running time (optimal speedup); the best previous algorithm achieves optimal speedup with a running time of O(log n log*n/log log n).

Keywords

Selection Problem Relative Accuracy Ranking Function Absolute Accuracy Search Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Shiva Chaudhuri
    • 1
  • Torben Hagerup
    • 1
  • Rajeev Raman
    • 2
  1. 1.Max-Planck-Institut für InformatikIm StadtwaldGermany
  2. 2.UMIACS, University of MarylandCollege Park

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