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arXiv · 1405.7828

Superconcentrators of Density 25.3

Vladimir Kolmogorov·Michal Rolinek
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Abstract

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. We prove the existence of such superconcentrators with asymptotic density $25.3$ (where the density is the number of edges divided by $N$). The previously best known densities were $28$ \cite{Scho2006} and $27.4136$ \cite{YuanK12}.

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Vladimir Kolmogorov, Michal Rolinek. 2014-05-30. Superconcentrators of Density 25.3. https://arxiv.org/abs/1405.7828

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