On embedding expanders into ℓ p spaces
- Cite this article as:
- Matoušek, J. Isr. J. Math. (1997) 102: 189. doi:10.1007/BF02773799
In this note we show that the minimum distortion required to embed alln-point metric spaces into the Banach space ℓ p is between (c 1/p) logn and (c 2/p) logn, wherec 2>c 1>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.