{"paper":{"title":"Constant Approximation of Fr\\'echet Distance in Strongly Subquadratic Time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Haoqiang Huang, Shuo Zhang, Siu-Wing Cheng","submitted_at":"2025-03-17T02:27:40Z","abstract_excerpt":"Let $\\tau$ and $\\sigma$ be two polygonal curves in $\\mathbb{R}^d$ for any fixed $d$. Suppose that $\\tau$ and $\\sigma$ have $n$ and $m$ vertices, respectively, and $m\\le n$. While conditional lower bounds prevent approximating the Fr\\'echet distance between $\\tau$ and $\\sigma$ within a factor of 3 in strongly subquadratic time, the current best approximation algorithm attains a ratio of $n^c$ in strongly subquadratic time, for some constant $c\\in(0,1)$. We present a randomized algorithm with running time $O(nm^{0.99}\\log(n/\\varepsilon))$ that approximates the Fr\\'echet distance within a factor "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.12746","kind":"arxiv","version":1},"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/2503.12746/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"}