The fat-pyramid and universal parallel computation independent of wire delay

This paper shows that a fat-pyramid of area /spl Theta/(A) requires only O(log A) slowdown to simulate any competing network of area A under very general conditions. The result holds regardless of the processor size (amount of attached memory) and number of processors in the competing networks as lo...

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Bibliographic Details
Published in:IEEE transactions on computers 1994-12, Vol.43 (12), p.1358-1364
Main Author: Greenberg, R.I.
Format: Article
Language:English
Subjects:
Applied sciences
Channel capacity
Computational modeling
Computer networks
Computer science
control theory
systems
Computer systems and distributed systems. User interface
Concurrent computing
Delay
Electric, optical and optoelectronic circuits
Electronics
Exact sciences and technology
Routing
Scheduling
Software
Software engineering
Switches
Transmission line theory
Wire
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Summary:This paper shows that a fat-pyramid of area /spl Theta/(A) requires only O(log A) slowdown to simulate any competing network of area A under very general conditions. The result holds regardless of the processor size (amount of attached memory) and number of processors in the competing networks as long as the limitation on total area is met. Furthermore, the result is valid regardless of the relationship between wire length and wire delay. We especially focus on elimination of the common simplifying assumption that unit time suffices to traverse a wire regardless of its length, since the assumption becomes more and more untenable as the size of parallel systems increases. This paper concentrates on simulation using transmission lines (wires along which bits can be pipelined) with the message routing schedule set up off line, but it also discusses the extension to on-line simulation. This paper also examines the capabilities of a fat-pyramid when matched against a substantially larger network and points out the surprising difficulty of doing such a comparison without the unit wire delay assumption.< >
ISSN:0018-9340
1557-9956
DOI:10.1109/12.338095