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Computing

, Volume 57, Issue 3, pp 245–253 | Cite as

A parametric algorithm for semigroup computation on mesh with buses

  • K. -L. Chung
  • Y. -C. Lin
Article

Abstract

In this paper, we present a new parametric parallel algorithm for semigroup computation on mesh with reconfigurable buses (MRB). Givenn operands, our parallel algorithm can be performed in\(O(2^{(2c^2 + 3c)/(4c + 1)} n^{1/(8c + 2)} )\), time on a\(2^{(c^2 - c)/(8c + 2)} n^{(5c + 1)/(8c + 2)} \times 2^{(c - c^2 )/(8c + 2)} n^{(3c + 1)/(8c + 2)} \) MRB ofn processors, where\(0 \leqslant c \leqslant O(\sqrt {\log _2 n} )\). Specifically, whenc=0, it takes\(O(\sqrt n )\) time on the\(\sqrt n \times \sqrt n \) MRB and is equal to the result on the mesh-connected computers; whenc=1, it takesO(n1/10) time on then3/5×n2/5 MRB and is equal to the previous result on the mesh-connected computers with segmented multiple buses; whenc=2, it takesO(n1/18) time on the 21/9n11/18×2(−1/9)n7/18 MRB; when\(O(\sqrt {\log _2 n} )\), it takesO(log2n) time and is equal to the previous result on the MRB. Consequently, our results can be viewed as a unification of some best known results on different parallel computational models.

AMS Subject Classifications

68Q20 90C39 65F 

Key words

Semigroup computation broadcasting mesh-connected computers with segmented buses reconfigurable buses parametric parallel algorithm 

Ein parametrisierter Algorithmus für die Halbgruppenberechnung auf Gittern mit Bussen

Zusammenfassung

Wir stellen einen Algorithmus für die Halbgruppenberechnung auf Gittern mit rekonfigurierbaren Bussen (MRB) vor. Mitn Operanden kann unser Algorithmus in\(O(2^{(2c^2 + 3c)/(4c + 1)} n^{1/(8c + 2)} )\) Zeit ausgeführt werden, wennn Prozessoren in einem\(2^{(c^2 - c)/(8c + 2)} n^{1/(5c + 1)/(8c + 2)} \times 2^{(c - c^2 )/(8c + 2)} n^{(3e + 1)/(8c + 2)} \) MRB-Gitter zur Verfügung stehen. Dabei gilt\(0 \leqslant c \leqslant O(\sqrt {\log _2 n} )\). Fürc=0 bedeutet dies\(O(\sqrt n )\) Zeit für den\(\sqrt n \times \sqrt n \) MRB und stimmt mit dem Wert für Gitter ohne Busse überein; fürc=1 ist nurO(n1/10) Zeit für einenn3/5×n2/5 MRB erforderlich, was mit einem früheren Ergebnis für Berechnung auf Gittern mit mehreren segmentierten Bussen übereinstimmt; fürc=2 istO(n1/18) Zeit für einen 21/9n11/18×2−1/9n7/18 MRB erforderlich; für\(c = O(\sqrt {\log _2 n} )\) istO(log2n) Zeit erforderlich, was auch mit dem früheren Ergebnis über MRB übereinstimmt. Unsere Resultate können also als vereinheitlichte Darstellung der bekanntesten Ergebnisse bei verschiedenen Modellen des Parallel-Computing angesehen werden.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • K. -L. Chung
    • 1
  • Y. -C. Lin
    • 1
  1. 1.Department of Information ManagementTaipeiTaiwan, R.O.C.

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