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Construction of expanders and superconcentrators using Kolmogorov complexity

✍ Scribed by Uwe Schöning

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
140 KB
Volume
17
Category
Article
ISSN
1042-9832

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✦ Synopsis

We show the existence of various versions of expander graphs using Kolmogorov complexity. This method seems superior to the usual probabilistic construction. It turns out that the best known bounds on the size of expanders and superconcentrators can be attained based on this method. In the case of (acyclic) superconcentrators we attain a density of about 34 edges/vertices. Furthermore, related graph properties are reviewed, like magnification, edge-magnification, and isolation, and we develop bounds based on the Kolmogorov approach.

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