STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
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A bipartite graph Gn = (U, V, E) is said an (n, k, &dgr;) expander if |U| = |V| = n, |E| ≤ kn, and for any X ⫅ U, |&Ggr;Gn(X)| ≥ (1+&dgr;(1-|X|/n)) |X|, where &Ggr;Gn(X) is the set of nodes in V connected to nodes in X with edges in E. In this paper we show that the problem of estimating the coefficient &dgr; of a bipartite graph is reduced to that of estimating the eigenvalue of a matrix related to the graph. As a result we give an explicit construction of (n, 5, 1 - 5/8 √2) expanders. By applying Gabber and Galil's construction to these expanders we obtain n-superconcentrators with 248n edges.