On embedding expanders into ℓp spaces
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In this note we show that the minimum distortion required to embed alln-point metric spaces into the Banach space ℓp is between (c1/p) logn and (c2/p) logn, wherec2>c1>0 are absolute constants and 1≤p<logn. The lower bound is obtained by a generalization of a method of Linial et al. [LLR95], by showing that constant-degree expanders (considered as metric spaces) cannot be embedded any better.
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