Elsevier

Information Processing Letters

Volume 23, Issue 3, 22 October 1986, Pages 123-126
Information Processing Letters

Efficient selection on a binary tree

https://doi.org/10.1016/0020-0190(86)90110-9Get rights and content

Abstract

Given a sequence of n ordered but not sorted b-bit integers, an algorithm is described to select the kth smallest by reducing the length of the original sequence until only the required kth value or those equal to the kth remain. Using the time to add two bits as the unit, a running time of O(b log n) is obtained by employing O(n) simple processors arranged in a binary tree. The algorithm is then adapted to run on a binary tree of processors with N leaves, where N log N ⩽ n, in O(bn/N) time for an optimal cost of O(bn).

References (6)

  • S.G. Akl

    An optimal algorithm for parallel selection

    Inform. Process. Lett.

    (1984)
  • A. Aggarwal

    A comparative study of X-tree, pyramid and related machines

  • M. Blum et al.

    Time bounds for selection

    J. Comput. System Sci.

    (1972)
There are more references available in the full text version of this article.

Cited by (6)

  • Optimal binary search trees

    1997, Theoretical Computer Science
  • An efficient selection algorithm on the pyramid

    1995, Information Processing Letters
  • Optically Interconnected Processor Arrays with Switching Capability

    1994, Journal of Parallel and Distributed Computing
  • On the bit complexity of parallel computations

    1988, Integration, the VLSI Journal
  • Embedding Binary X-Trees and Pyramids in Processor Arrays with Spanning Buses

    1994, IEEE Transactions on Parallel and Distributed Systems
  • A Nonsorting Vlsi Structure for Implementing the (M, L) Algorithm

    1988, IEEE Journal on Selected Areas in Communications

This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-3336.

View full text