{"paper":{"title":"Incremental Voronoi Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"John Iacono, Luis Barba, Sarah R. Allen, Stefan Langerman","submitted_at":"2016-03-28T18:59:36Z","abstract_excerpt":"We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram $\\mathcal{V}(S)$ (and several variants thereof) of a set $S$ of $n$ sites in the plane as sites are added.\n  We define a general update operation for planar graphs modeling the incremental construction of several variants of Voronoi diagrams as well as the incremental construction of an intersection of halfspaces in $\\mathbb{R}^3$. We show that the amortized number of edge insertions and removals needed to add a new site is $O(\\sqrt{n})$. A matching "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08485","kind":"arxiv","version":1},"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"}