We prove that every n-point metric space of negative type (in particular, every n-point subset of L1) embeds into a Euclidean space with distortion O(âˆšlog n log log n), a result which is tight up toâ€¦ (More)

For every d > 0, let k<inf>d</inf> be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n,d/n) is either k<inf>d</inf> or k<inf>d+1</inf> almostâ€¦ (More)

It is widely believed that for many optimization problems, no algorithm is substantially more efficient than exhaustive search. This means that finding optimal solutions for many practical problemsâ€¦ (More)

It is shown that if X1, X2, . . . are independent and identically distributed square-integrable random variables then the entropy of the normalized sum Ent ( X1 + Â· Â· Â·+ Xn âˆš n ) is an increasingâ€¦ (More)

We introduce a new graph parameter, called the <i>Grothendieck constant</i> of a graph <i>G</i>=(<i>V,E</i>), which is defined as the least constant <i>K</i> such that for everyâ€¦ (More)

Various new nonembeddability results (mainly into L/sub 1/) are proved via Fourier analysis. In particular, it is shown that the edit distance on {0, 1}/sup d/ has L/sub 1/ distortion (log d)/sup 1/2â€¦ (More)

In this article we introduce the notion of nearest-neighbor-preserving embeddings. These are randomized embeddings between two metric spaces which preserve the (approximate) nearest-neighbors. Weâ€¦ (More)