Randomness conductors and constant-degree lossless expanders

Michael Capalbo*, Omer Reingold, Salil Vadhan, Avi Wigderson

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

192 Scopus citations

Abstract

The main concrete result of this paper is the first explicit construction of constant degree lossless expanders. In these graphs, the expansion factor is almost as large as possible: (1 = ε) D, where D is the degree and ε is an arbitrarily small constant. The best previous explicit constructions gave expansion factor D/2, which is too weak for many applications. The D/2 bound was obtained via the eigenvalue method, and is known that method cannot give better bounds. The main abstract contribution of this paper is the introduction and initial study of randomness conductors, a notion which generalizes extractors, expanders, condensers and other similar objects. In all these functions, certain guarantee on the input "entropy" is converted to a guarantee on the output "entropy". For historical reasons, specific objects used specific guarantees of different flavors. We show that the flexibility afforded by the conductor definition leads to interesting combinations of these objects, and to better constructions such as those above.

Original languageEnglish
Pages (from-to)659-668
Number of pages10
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs
StatePublished - 2002
EventProceedings of the 34th Annual ACM Symposium on Theory of Computing - Montreal, Que., Canada
Duration: 19 May 200221 May 2002

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