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An Elementary Construction of Constant-Degree Expanders

Published online by Cambridge University Press:  01 May 2008

NOGA ALON ,
ODED SCHWARTZ  and
ASAF SHAPIRA
NOGA ALON
Affiliation:
Schools of Mathematics and Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: nogaa@tau.ac.il)
ODED SCHWARTZ
Affiliation:
School of Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: odedsc@tau.ac.il, asafico@tau.ac.il)
ASAF SHAPIRA
Affiliation:
School of Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: odedsc@tau.ac.il, asafico@tau.ac.il)
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Abstract

We describe a short and easy-to-analyse construction of constant-degree expanders. The construction relies on the replacement product, applied by Reingold, Vadhan and Wigderson (2002) to give an iterative construction of bounded-degree expanders. Here we give a simpler construction, which applies the replacement product (only twice!) to turn the Cayley expanders of Alon and Roichman (1994), whose degree is polylog n, into constant-degree expanders. This enables us to prove the required expansion using a simple new combinatorial analysis of the replacement product (instead of the spectral analysis used by Reingold, Vadhan and Wigderson).

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 3 , May 2008 , pp. 319 - 327
Copyright
Copyright © Cambridge University Press 2008

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