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Theory of Computing Systems

, Volume 32, Issue 5, pp 531–559 | Cite as

Processor—Time Tradeoffs under Bounded-Speed Message Propagation: Part II, Lower Bounds

  • G. Bilardi
  • F. P. Preparata

Abstract.

Lower bounds are developed for the processor—time tradeoffs of machines such as linear arrays and two-dimensional meshes, which are compatible with the physical limitation on propagation speed of messages. The machines we consider are characterized by the property that identical numbers of simultaneous memory accesses, operations, and message communications are expressed by the number of processors. For this class of machines, a class of computations is analyzed for which parallelism and locality combined yield speedups superlinear in the number of processors. The results are obtained by means of a novel technique, called the ``closed-dichotomy-size technique,'' designed to obtain lower bounds to the computation time for networks of processors, each of which is equipped with a local hierarchical memory.

Keywords

Lower Bound Computation Time Memory Access Linear Array Physical Limitation 
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 New York Inc. 1999

Authors and Affiliations

  • G. Bilardi
    • 1
  • F. P. Preparata
    • 2
  1. 1.DEI, Università di Padova, Padova, Italy bilardi@artemide.dei.unipd.it and EECS, University of Illinois, Chicago, IL 60607, USA IT
  2. 2.Department of Computer Science, Brown University, 115 Waterman, Providence, RI 02912-1910, USA franco@cs.brown.eduUS

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