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The \\emph{dual graph} $\\triang^*$ of a triangulation~$\\triang$ of~$\\Poly$ is the graph whose vertices correspond to the bounded faces of $\\triang$ and whose edges connect those faces of~$\\triang$ that share an edge. We consider triangulations of~$\\Poly$ that minimize or maximize the diameter of their dual graph. We show that both triangulations can be constructed in $O(n^3\\log n)$ time using dynamic programming. If $\\Poly$ is convex, we show that any minimizing triangulation has dual diameter exactly $2\\cdot\\lceil\\log_2(n/3)\\rceil$ or $2\\cdot\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.08518","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-03-30T01:36:22Z","cross_cats_sorted":[],"title_canon_sha256":"384ce04a2de22d3c9f438b06b283370334f840b53e3ca06e9a1f3b5fa0a21b7d","abstract_canon_sha256":"c485e85871e05514a217a85a3baafce59c0511f0ec725036339cdf554d524847"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:52.421793Z","signature_b64":"7oZm3WsHIc/bS71/omo5ZY3MYjy5/ECvdwSDj8382EZeTyxrmH3lv17AJmzedQ4yyehbaDrNaJ7HwUa7gk7mDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb8ddf2706a618c1eabb8dea3a855bfa5d6e45e63ebadaca3045a23b17b1cf5b","last_reissued_at":"2026-05-18T00:31:52.421081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:52.421081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Dual Diameter of Triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alexander Pilz, Birgit Vogtenhuber, Maria Saumell, Matias Korman, Stefan Langerman, Wolfgang Mulzer","submitted_at":"2015-03-30T01:36:22Z","abstract_excerpt":"Let $\\Poly$ be a simple polygon with $n$ vertices. 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