Deterministic selection in O(loglog N) parallel time
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Explicit expanders and the Ramanujan conjectures
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Deterministic simulation in LOGSPACE
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Sorting in c log n parallel steps
Combinatorica
A note on time-space tradeoffs for computing continuous functions
Information Processing Letters
Graph-theoretic properties in computational complexity
Journal of Computer and System Sciences
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We present an algorithm which in n3(log n)3 time constructs a 3- regular expander graph on n vertices. In each step we substitute a pair of edges of the graph by a new pair of edges so that the total number of cycles of length s = [c log n] decreases (for some fixed absolute constant c). When we reach a local minimum in the number of cycles of length s the graph is an expander. The proof is completely elementary, we use only the basic results about the eigenvalues and eigenvectors of symmetric matrices.