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Parallel contraction of fibonacci trees and prefix computations on a family of interconnection topologies

  • W. -J. Hsu
  • C. V. Page
  • J. Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 581)

Abstract

The computation of prefixes of a given sequence (prefix computation [14]) and the fast reduction of a tree to a single node (tree contraction [1]) are two useful primitives for many applications on parallel computers. Most previous parallel algorithms have been based on the shared-memory model. We present general parallel algorithms for reducing a class of trees and prefix computations under the distributed-memory model. The new algorithms are shown to be communication-efficient and suitable for a large family of parallel computers. This family of parallel computers are based on a novel interconnection topology called the p-th order Fibonacci cube [10] that generalizes the Boolean cube (hypercube) [18] and the (second order) Fibonacci cube [8]. Specifically, the following results are presented:
  1. 1.

    We show that the p-th order Fibonacci tree of size N can be reduced to a single node in O(log N) steps on a p-th order Fibonacci cube with N nodes (processors).

     
  2. 2.

    Assume that O(log N) data items are on each of the N processors. We show that the prefix computation can be done in O(log N) steps on the p-th order Fibonacci cube.

     

Keywords

Data Item Binary Code Partial Product Binomial Tree Interconnection Topology 
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 1992

Authors and Affiliations

  • W. -J. Hsu
    • 1
  • C. V. Page
    • 1
  • J. Liu
    • 1
  1. 1.Dept. of Computer ScienceMichigan State UniversityUSA

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