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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1993: STACS 93 pp 294–305Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((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/logk n) 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(log3 n) time using n 2/log3 n processors on a CREW PRAM.

We also consider the problem of finding an optimal triangulation in a monotone polygon. An O(log2 n) time and n processors algorithm on a CREW PRAM is given.

Supported in part by the EC Cooperative Action IC 1000 Algorithms for Future Technologies “ALTEC” and by the grant KBN 2-1190-91-01.

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Authors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Artur Czumaj

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  1. Artur Czumaj
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P. Enjalbert A. Finkel K. W. Wagner

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© 1993 Springer-Verlag Berlin Heidelberg

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Czumaj, A. (1993). Parallel algorithm for the matrix chain product and the optimal triangulation problems (extended abstract). In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_30

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  • DOI: https://doi.org/10.1007/3-540-56503-5_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56503-1

  • Online ISBN: 978-3-540-47574-3

  • eBook Packages: Springer Book Archive

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