Optimal broadcast on parallel locality models

  • Authors:

  • Ben Juurlink;Petr Kolman;Friedhelm Meyer auf der Heide;Ingo Rieping

  • Affiliations:

  • Faculty of Electrical Engineering, Mathematics and Computer Sciences, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;Institute for Theoretical Computer Science, Charles University, Malostranské nám. 25, 118 00 Prague, Czech Republic;Heinz Nixdorf Institute and Department of Mathematics and Computer Science, Paderborn University, Fürstenallee 11, 33102 Paderborn, Germany;Heinz Nixdorf Institute and Department of Mathematics and Computer Science, Paderborn University, Fürstenallee 11, 33102 Paderborn, Germany

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2003

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Abstract

In this paper matching upper and lower bounds for broadcast on general purpose parallel computation models that exploit network locality are proven. These models try to capture both the general purpose properties of models like the PRAM or BSP on the one hand, and to exploit network locality of special purpose models like meshes, hypercubes, etc., on the other hand. They do so by charging a cost l (|i - j|) for a communication between processors i and j, where l is a suitably chosen latency function.An upper bound T (p) = Σi=0loglog p 2i ċ l(p1/2i) on the runtime of a broadcast on a p processor H-PRAM is given, for an arbitrary latency function l(k).The main contribution of the paper is a matching lower bound, holding for all latency functions in the range from l (k) = Ω (log k/log log k) to l (k) = O (log2 k). This is not a severe restriction since for latency functions l(k) = O(logk/log1+ε log(k)) with arbitrary ε 0, the runtime of the algorithm matches the trivial lower bound Ω(log p) and for l(k) = Θ (log 1+ε k) or l(k) = Θ(kε), the runtime matches the other trivial lower bound Ω(l(p)). Both upper and lower bounds apply for other parallel locality models like Y-PRAM, D-BSP and E-BSP, too.