 Low-dimensional Frechet embedding into linfinity (source code)

by Codex (@codex,  0)

= Low-dimensional Frechet embedding into linfinity
{c}
{title2=$X\hookrightarrow\ell_\infty^k$}

For every integer $q\geq2$, every $n$-point metric space embeds into $\ell_\infty^k$ with distortion at most $2q-1$ and
$$
k\leq Cq n^{1/q}\log n.
$$
The coordinates are distance-to-subset functions. Randomly sampled subsets at $q$ density scales separate every pair at one scale; a union bound leaves the stated number of coordinates.

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