The Power of Recursive Embeddings for $\ell_p$ Metrics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909568053805056 |
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| author | Krauthgamer, Robert Petruschka, Nir Sapir, Shay |
| author_facet | Krauthgamer, Robert Petruschka, Nir Sapir, Shay |
| contents | Metric embedding is a powerful tool used extensively in mathematics and computer science. We devise a new method of using metric embeddings recursively, which turns out to be particularly effective in $\ell_p$ spaces, $p>2$, yielding state-of-the-art results for Lipschitz decomposition, for Nearest Neighbor Search, and for embedding into $\ell_2$. In a nutshell, our method composes metric embeddings by viewing them as reductions between problems, and thereby obtains a new reduction that is substantially more effective than the known reduction that employs a single embedding. We in fact apply this method recursively, oftentimes using double recursion, which further amplifies the gap from a single embedding. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_18508 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Power of Recursive Embeddings for $\ell_p$ Metrics Krauthgamer, Robert Petruschka, Nir Sapir, Shay Computational Geometry Data Structures and Algorithms Metric Geometry Metric embedding is a powerful tool used extensively in mathematics and computer science. We devise a new method of using metric embeddings recursively, which turns out to be particularly effective in $\ell_p$ spaces, $p>2$, yielding state-of-the-art results for Lipschitz decomposition, for Nearest Neighbor Search, and for embedding into $\ell_2$. In a nutshell, our method composes metric embeddings by viewing them as reductions between problems, and thereby obtains a new reduction that is substantially more effective than the known reduction that employs a single embedding. We in fact apply this method recursively, oftentimes using double recursion, which further amplifies the gap from a single embedding. |
| title | The Power of Recursive Embeddings for $\ell_p$ Metrics |
| topic | Computational Geometry Data Structures and Algorithms Metric Geometry |
| url | https://arxiv.org/abs/2503.18508 |