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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","authors_text":"Cyril Gavoille (LaBRI, INRIA Bordeaux - Sud-Ouest, INRIA Bordeaux - Sud-Ouest), IUF), Ljubomir Perkovic (CTI, Nicolas Bonichon (LaBRI, Nicolas Hanusse (LaBRI, SOC)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-02-23T09:19:35Z","title":"The Stretch Factor of $L_1$- and $L_\\infty$-Delaunay Triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5127","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:449a9f0e98b9d13c32fef5567624eb9744973947d241646621cc2bd5095be417","target":"record","created_at":"2026-05-18T04:01:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a163bc85e08417b0d2bf77bf7fccabf06d34be61fea2c2046e5b0a0233f5b433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-02-23T09:19:35Z","title_canon_sha256":"5276a809a275bb94318d0640eefdd2f750fb1822bc9f962119392437eb5eb289"},"schema_version":"1.0","source":{"id":"1202.5127","kind":"arxiv","version":2}},"canonical_sha256":"f9727bd10d7c398a432d291e1d7f5c7b9289171b43bbeea82979d265ad0d9a0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9727bd10d7c398a432d291e1d7f5c7b9289171b43bbeea82979d265ad0d9a0b","first_computed_at":"2026-05-18T04:01:25.415364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:25.415364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZOKY+hmlxvVCCrll0rGF3oPaMx92QKHozrItRtN/n3V0eJYqVa8t0xFrjnS76zA2/nLyCrgJU+HcRatzxXicCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:25.416072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5127","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:449a9f0e98b9d13c32fef5567624eb9744973947d241646621cc2bd5095be417","sha256:4747c40ee1329f32459cc416a6acf4f673c682b6981d80d8e437a13681469212"],"state_sha256":"5b776884d59e7a7ebc847f69c9f8800442b9fd2640eedad11f5c5bea59ee6294"}