2026-08-17T03:26:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19961 2024-06-06T06:21:13Z ddc:004 open_access

A Coreset for Approximate Furthest-Neighbor Queries in a Simple Polygon de Berg, Mark Theocharous, Leonidas Furthest-neighbor queries polygons geodesic distance coreset Let 𝒫 be a simple polygon with m vertices and let P be a set of n points inside 𝒫. We prove that there exists, for any ε > 0, a set C ⊂ P of size O(1/ε²) such that the following holds: for any query point q inside the polygon 𝒫, the geodesic distance from q to its furthest neighbor in C is at least 1-ε times the geodesic distance to its further neighbor in P. Thus the set C can be used for answering ε-approximate furthest-neighbor queries with a data structure whose storage requirement is independent of the size of P. The coreset can be constructed in O(1/(ε) (nlog(1/ε) + (n+m)log(n+m))) time. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mark de Berg and Leonidas Theocharous 2024 Is Part Of LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2024.16 urn:nbn:de:0030-drops-199613 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.16 eng https://creativecommons.org/licenses/by/4.0/legalcode