{"paper":{"title":"The Stretch Factor of $L_1$- and $L_\\infty$-Delaunay Triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Cyril Gavoille (LaBRI, INRIA Bordeaux - Sud-Ouest, INRIA Bordeaux - Sud-Ouest), IUF), Ljubomir Perkovic (CTI, Nicolas Bonichon (LaBRI, Nicolas Hanusse (LaBRI, SOC)","submitted_at":"2012-02-23T09:19:35Z","abstract_excerpt":"In this paper we determine the stretch factor of the $L_1$-Delaunay and $L_\\infty$-Delaunay triangulations, and we show that this stretch is $\\sqrt{4+2\\sqrt{2}} \\approx 2.61$. Between any two points $x,y$ of such triangulations, we construct a path whose length is no more than $\\sqrt{4+2\\sqrt{2}}$ times the Euclidean distance between $x$ and $y$, and this bound is best possible. This definitively improves the 25-year old bound of $\\sqrt{10}$ by Chew (SoCG '86). To the best of our knowledge, this is the first time the stretch factor of the well-studied $L_p$-Delaunay triangulations, for any rea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5127","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":""},"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"}