Metraipolis › archive › dc_bb3fdebf7447

Optimal Average Distortion for Non-Expansive Embeddings of Euclidean Metrics into the Line: With applications to cut-matching games and vertex expansion — arXiv:2610.41945

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41945
License (as archived): CC0-1.0
Archived: 2026-11-03T05:49:22.694Z
SHA-256 of the archived text: 949ae8436cc1e83359f4063b0a88d9ede524c9ed17e92086e23ab7a6b7eb559a
Stable URL of this page: https://metraipolis.com/documento/dc_bb3fdebf7447

How to cite

Optimal Average Distortion for Non-Expansive Embeddings of Euclidean Metrics into the Line: With applications to cut-matching games and vertex expansion — arXiv:2610.41945 — arXiv (en), https://arxiv.org/abs/2610.41945 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bb3fdebf7447 (Metraipolis archive dc_bb3fdebf7447, sha256 949ae8436cc1e83359f4063b0a88d9ede524c9ed17e92086e23ab7a6b7eb559a)

BibTeX

@misc{dcbb3fdebf7447,
  title = {Optimal Average Distortion for Non-Expansive Embeddings of Euclidean Metrics into the Line: With applications to cut-matching games and vertex expansion — arXiv:2610.41945},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41945},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bb3fdebf7447; sha256 949ae8436cc1e83359f4063b0a88d9ede524c9ed17e92086e23ab7a6b7eb559a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41945. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We show that any $n$-point Euclidean metric admits a non-expansive embedding into the line with average distortion at most $O\left(\sqrt{\frac{\log n}{\log\log n}}\right)$, matching a known lower bound. We also present two applications of this result. First, we give a cut-player strategy with an optimal spectral guarantee for the undirected cut-matching game. Second, we give an improved spectral approximation for vertex expansion in high-degree graphs.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv cs.DS, nuovi lavori del giorno).
Categorie arXiv: Data Structures and Algorithms (cs.DS) ; Computational Geometry (cs.CG); Metric Geometry (math.MG).
Pagina del lavoro: https://arxiv.org/abs/2610.41945 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T05:34:47.024Z dalla pagina https://arxiv.org/list/cs.DS/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).