{"paper":{"title":"Dynamic Metric Embedding into $\\ell_p$ Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dariusz R. Kowalski, Jan Olkowski, Kiarash Banihashem, Max Springer, MohammadTaghi Hajiaghayi","submitted_at":"2024-06-25T01:41:48Z","abstract_excerpt":"We give the first non-trivial decremental dynamic embedding of a weighted, undirected graph $G$ into $\\ell_p$ space. Given a weighted graph $G$ undergoing a sequence of edge weight increases, the goal of this problem is to maintain a (randomized) mapping $\\phi: (G,d) \\to (X,\\ell_p)$ from the set of vertices of the graph to the $\\ell_p$ space such that for every pair of vertices $u$ and $v$, the expected distance between $\\phi(u)$ and $\\phi(v)$ in the $\\ell_p$ metric is within a small multiplicative factor, referred to as the \\emph{distortion}, of their distance in $G$. Our main result is a dyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.17210","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.17210/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}