Fox, G. C. and Furmanski, W. (1988) Load balancing loosely synchronous problems with a neural network. In: C3P Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues. Vol.1. ACM , New York, NY, pp. 241-278. ISBN 0-89791-278-0. https://resolver.caltech.edu/CaltechAUTHORS:20161024-153822707
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Abstract
Hopfield and Tank have introduced the use of neural networks for the solution of optimization problems such as the traveling salesman problem. Here we show how to generalize this method to decompose loosely synchronous problems onto parallel machines and in particular the hypercube. In this case, decomposition or load balancing can be formulated graph theoretically in terms of optimal partitioning of the computational graph into N = 2d subgraphs. The algorithm has a suggestive spin system interpretation, with the ferromagnetic interaction minimizing the communication and the long range paramagnetic force balancing the load. The optimal fixed point of the network is in the Higgs phase of the magnet, with the domains of constant spontaneous magnetization representing the optimal decomposition map. The method is fast, reliable and admits various simple implementations: sequential, concurrent on the hypercube, analog on the neural network with adaptive weights (“learning”). We analyze the sequential performance of various mean field based network algorithms and we compare the network approach with the statistical Monte Carlo technique of simulated annealing.
Item Type: | Book Section | ||||||||||||
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Additional Information: | © 1988 ACM. Work supported in part by DOE grant DE-FG03-85ER25009, the Program Manager of the Joint Tactical Fusion Office, and the ESD division of the USAF, as well as grants from IBM, and SANDIA. | ||||||||||||
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DOI: | 10.1145/62297.62327 | ||||||||||||
Record Number: | CaltechAUTHORS:20161024-153822707 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20161024-153822707 | ||||||||||||
Official Citation: | G. C. Fox and W. Furmanski. 1988. Load balancing loosely synchronous problems with a neural network. In Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues - Volume 1 (C3P), Geoffrey Fox (Ed.), Vol. 1. ACM, New York, NY, USA, 241-278. DOI=http://dx.doi.org/10.1145/62297.62327 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 71411 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Kristin Buxton | ||||||||||||
Deposited On: | 24 Oct 2016 22:47 | ||||||||||||
Last Modified: | 11 Nov 2021 04:44 |
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