Explicit Bounded-Degree Unique-Neighbor Concentrators |
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Authors: | Michael Capalbo |
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Institution: | (1) Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD;(2) School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA |
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Abstract: | Here we solve an open problem considered by various researchers by presenting the first explicit constructions of an infinite
family
of bounded-degree ‘unique-neighbor’ concentrators Γ; i.e., there are strictly positive constants α and ε, such that all Γ = (X,Y,E(Γ)) ∈
satisfy the following properties. The output-set Y has cardinality
times that of the input-set X, and for each subset S of X with no more than α|X| vertices, there are at least ε|S| vertices in Y that are adjacent in Γ to exactly one vertex in S. Also, the construction of
is simple to specify, and each
has fewer than
edges. We then modify
to obtain explicit unique-neighbor concentrators of maximum degree 3.
* Supported by NSF grant CCR98210-58 and ARO grant DAAH04-96-1-0013. |
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Keywords: | 05C35 |
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