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

@article{Reingold2000EntropyWT,
  title={Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors},
  author={Omer Reingold and Salil P. Vadhan and Avi Wigderson},
  journal={Proceedings 41st Annual Symposium on Foundations of Computer Science},
  year={2000},
  pages={3-13}
}
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… 
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