An elementary construction of constant-degree expanders

Authors:
Noga Alon;Oded Schwartz;Asaf Shapira
Affiliations:
Tel Aviv University, Tel Aviv, Israel;Tel Aviv University, Tel Aviv, Israel;Microsoft Research
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

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Abstract

We describe a short and easy to analyze construction of constant-degree expanders. The construction relies on the replacement product, applied by [14] 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 [4], whose degree is polylog n, into constant degree expanders. This enables us to prove the required expansion using a new simple combinatorial analysis of the replacement product (instead of the spectral analysis used in [14]).