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arXiv · 2110.03152

Optimal (Euclidean) Metric Compression

Piotr Indyk·Tal Wagner
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Abstract

We study the problem of representing all distances between $n$ points in $\mathbb R^d$, with arbitrarily small distortion, using as few bits as possible. We give asymptotically tight bounds for this problem, for Euclidean metrics, for $\ell_1$ (a.k.a.~Manhattan) metrics, and for general metrics. Our bounds for Euclidean metrics mark the first improvement over compression schemes based on discretizing the classical dimensionality reduction theorem of Johnson and Lindenstrauss (Contemp.~Math.~1984). Since it is known that no better dimension reduction is possible, our results establish that Euclidean metric compression is possible beyond dimension reduction.

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Piotr Indyk, Tal Wagner. 2021-10-07. Optimal (Euclidean) Metric Compression. https://arxiv.org/abs/2110.03152

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