An Elementary Construction of Constant-Degree Expanders

Author:

ALON NOGA,SCHWARTZ ODED,SHAPIRA ASAF

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).

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science

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