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Feb 1, 2010 at 18:13 vote accept Donald
Jan 30, 2010 at 18:31 comment added Bill Johnson The Brinkman-Charikar examples are the diamond graphs, which live in the Hamming cube. The only positive result for $\ell_1$ is that $n$ vectors well embed into $\ell_1^k$ with $k$ of order $n\log$n! Probably you know that you can do what you want if you are in $\ell_2$; if not, Google "Johnson-Lindenstrauss Lemma".
Jan 29, 2010 at 23:28 history answered Suresh Venkat CC BY-SA 2.5