By Topic

A fractal analysis of interconnection complexity

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
P. Christie ; Dept. of Electr. Eng., Delaware Univ., Newark, DE, USA

The emergent, collective properties of computer interconnections are shown to be characterized by a noninteger dimension Di , which is, in general, different from the system's Euclidean dimension. This dimension characterizes the properties of a fractal support, or substrate, on which interconnections are placed to provide communication throughout the system. The interconnection support also acts as a host for a multifractal spectrum of interconnection distribution processes which characterize the change in connectivity in moving from the backplane to the transistor level. The properties of fractal systems are investigated by attempting to minimize their total wire length using a simulated annealing algorithm. Systems whose interconnection dimension is approximately equal to their Euclidean dimension are shown to possess minimum wire length arrangements. These results are then interpreted in terms of a geometrical temperature T i=1/Di. This analysis indicates that the system passes through a phase transition at Ti≈1/2 and that attainable system temperatures are bounded by 1/3⩽Ti⩽1. The consequences for simulated annealing are discussed

Published in:

Proceedings of the IEEE  (Volume:81 ,  Issue: 10 )