{"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. 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\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08518","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"}