• Journal of Korea Multimedia Society
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• v.3 no.6
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• pp.674-684
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• 2000

One key obstacle which has been identified in achieving parallel processing is to communicate effectively between processors during execution. One approach to achieving an optimal delay time is to use expander graph. The networks and algorithms which are based on expander graphs are successfully exploited to yield fast parallel algorithms and efficient design. The AKS sorting algorithm in time O(logN) which is an important result is based on the use of expanders. The expander graph also can be applied to construct a concentrator and a superconcentrator. Since Margulis found a way to construct an explicit linear expander graph, several expander graphs have been developed. But the proof of existence of such graphs is in fact provided by a nonconstructive argument. We investigate the expander network on the hypercube network. We prove the expansion of a sin81e stage hypercube network and extend this from a single stage to multistage networks. The results in this paper provide a theoretical analysis of expansion in the hypercube network.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.9
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• pp.1939-1946
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• 2011

Expander graphs are useful in the design and analysis of communication networks. Mukhopadhyay et. al introduced a method to generate a family of expander graphs based on nongroup two predecessor single attractor CA(Cellular Automata). In this paper we propose a method to generate a family of expander graphs based on 60/102 Null boundary CA(NBCA) which is a group CA. The spectral gap generated by our method is larger than that of Mukhopadhyay et. al [12]. As an application we give an algorithm which generate one-way functions whose security lies on the combinatorial properties of our expander graphs. the one-way function using d-regular graph generated by the 60/102 NBCA is based on the Goldreich's construction [5].