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Parallel algorithm for the matrix chain product and the optimal triangulation problems (extended abstract)

  • Artur Czumaj
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)

Abstract

This paper considers the problem of finding an optimal order of the multiplication chain of matrices and the problem of finding an optimal triangulation of a convex polygon. For both these problems the best sequential algorithms run in ⊗(n log n) time. All parallel algorithms known use the dynamic programming paradigm and run in a polylogarithmic time using, in the best case, O(n6/logkn) processors for a constant k. We give a new algorithm which uses a different approach and reduces the problem to computing certain recurrence in a tree. We show that this recurrence can be optimally solved which enables us to improve the parallel bound by a few factors. Our algorithm runs in O(log3n) time using n2/log3n processors on a CREW PRAM.

We also consider the problem of finding an optimal triangulation in a monotone polygon. An O(log2n) time and n processors algorithm on a CREW PRAM is given.

Keywords

Parallel Algorithm Total Work Convex Polygon Marked Vertex Small Vertex 
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

  • Artur Czumaj
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarszawaPoland

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