{"paper":{"title":"Essential Constraints of Edge-Constrained Proximity Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alina Shaikhet, Jean-Lou De Carufel, Michiel Smid, Prosenjit Bose","submitted_at":"2016-07-05T15:22:34Z","abstract_excerpt":"Given a plane forest $F = (V, E)$ of $|V| = n$ points, we find the minimum set $S \\subseteq E$ of edges such that the edge-constrained minimum spanning tree over the set $V$ of vertices and the set $S$ of constraints contains $F$. We present an $O(n \\log n )$-time algorithm that solves this problem. We generalize this to other proximity graphs in the constraint setting, such as the relative neighbourhood graph, Gabriel graph, $\\beta$-skeleton and Delaunay triangulation. We present an algorithm that identifies the minimum set $S\\subseteq E$ of edges of a given plane graph $I=(V,E)$ such that $I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01294","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"}