Combinatorica
Lifts, Discrepancy and Nearly Optimal Spectral Gap
Combinatorica
On Construction of Almost-Ramanujan Graphs
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Graph expansion and communication costs of fast matrix multiplication: regular submission
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
On laplacians of random complexes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Graph expansion and communication costs of fast matrix multiplication
Journal of the ACM (JACM)
Graph expansion analysis for communication costs of fast rectangular matrix multiplication
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Communication costs of Strassen's matrix multiplication
Communications of the ACM
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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).