NDLI: Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors

Content Provider	IEEE Xplore Digital Library
Author	Reingold, O. Vadhan, S. Wigderson, A.
Copyright Year	2000
Description	Author affiliation: AT&T Labs.-Res., Florham Park, NJ, USA (Reingold, O.)
Abstract	The main contribution is a new type of graph product, which we call the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both. Iteration yields simple explicit constructions of constant-degree expanders of every size, starting from one constant-size expander. Crucial to our intuition (and simple analysis) of the properties of this graph product is the view of expanders as functions which act as "entropy wave" propagators-they transform probability distributions in which entropy is concentrated in one area to distributions where that concentration is dissipated. In these terms, the graph product affords the constructive interference of two such waves. A variant of this product can be applied to extractors, giving the first explicit extractors whose seed length depends (poly)logarithmically on only the entropy deficiency of the source (rather than its length) and that extract almost all the entropy of high min-entropy sources. These high min-entropy extractors have several interesting applications, including the first constant-degree explicit expanders which beat the "eigenvalue bound".
Starting Page	3
Ending Page	13
File Size	1085936
Page Count	11
File Format	PDF
ISBN	0769508502
ISSN	02725428
DOI	10.1109/SFCS.2000.892006
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2000-11-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Entropy Graph theory Eigenvalues and eigenfunctions Polynomials Probability distribution Mathematics Computer science Complexity theory Codes Cryptography
Content Type	Text
Resource Type	Article

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