{"paper":{"title":"A Gap-ETH-Tight Approximation Scheme for Euclidean TSP","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"cs.CG","authors_text":"Jesper Nederlof, Karol W\\k{e}grzycki, S\\'andor Kisfaludi-Bak","submitted_at":"2020-11-07T13:50:43Z","abstract_excerpt":"We revisit the classic task of finding the shortest tour of $n$ points in $d$-dimensional Euclidean space, for any fixed constant $d \\geq 2$. We determine the optimal dependence on $\\varepsilon$ in the running time of an algorithm that computes a $(1+\\varepsilon)$-approximate tour, under a plausible assumption. Specifically, we give an algorithm that runs in $2^{\\mathcal{O}(1/\\varepsilon^{d-1})} n\\log n$ time. This improves the previously smallest dependence on $\\varepsilon$ in the running time $(1/\\varepsilon)^{\\mathcal{O}(1/\\varepsilon^{d-1})}n \\log n$ of the algorithm by Rao and Smith~(STOC"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.03778","kind":"arxiv","version":3},"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/2011.03778/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"}