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Embedding the diamond graph in . . .

By James R. Lee and Assaf Naor


We show that any embedding of the level k diamond graph of Newman and Rabinovich [6] into Lp, 1 < p ≤ 2, requires distortion at least � k(p − 1) + 1. An immediate corollary is that there exist arbitrarily large n-point sets X ⊆ L1 such that any D-embedding of X into ℓ d 1 requires d ≥ n Ω(1/D2). This gives a simple proof of a recent result of Brinkman and Charikar [2] which settles the long standing question of whether there is an L1 analogue of the Johnson-Lindenstrauss dimension reduction lemma [4]

Year: 1990
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