Abstract
We study the problem of representing all distances between n points in Rd, with arbitrarily small distortion, using as few bits as possible. We give asymptotically tight bounds for this problem, for Euclidean metrics, for ℓ 1 (also known as 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. 26 (1984), pp. 189-206]. Since it is known that no better dimension reduction is possible, our results establish that Euclidean metric compression is possible beyond dimension reduction.
| Original language | English |
|---|---|
| Pages (from-to) | 467-491 |
| Number of pages | 25 |
| Journal | SIAM Journal on Computing |
| Volume | 51 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2022 |
| Externally published | Yes |
Keywords
- dimension reduction
- distance oracle
- distance sketch
- metric sketch
- quantization
All Science Journal Classification (ASJC) codes
- General Computer Science
- General Mathematics
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