On embedding expanders into ?
p
spaces |
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Authors: | Ji?í Matou?ek |
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Institution: | (1) Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic |
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Abstract: | 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.
Research supported by Czech Republic Grant GAČR 201/94/2167 and Charles University grants No. 351 and 361. |
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Keywords: | |
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