Journal of the ACM (JACM)
Construction of expanders and superconcentrators using Kolmogorov complexity
Random Structures & Algorithms
Resolution Proofs, Exponential Bounds, and Kolmogorov Complexity
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
On non-linear lower bounds in computational complexity
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
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An N-superconcentrator is a directed, acyclic graph with N input nodes and N output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known that linear-size and bounded-degree superconcentrators exist. Here it is proved that such superconcentrators exist (by a random construction of certain expander graphs as building blocks) having density 28 (where the density is the number of edges divided by N). The best known density before this paper was 34.2 [U. Schoning, Construction of expanders and superconcentrators using Kolmogorov complexity, J. Random Structures Algorithms 17 (2000) 64-77] or 33 [L.A. Bassalygo, Personal communication, 2004].