2026-07-20T11:15:28Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6827 2024-03-06T10:38:58Z ddc:004 open_access

Assigning Weights to Minimize the Covering Radius in the Plane Oh, Eunjin Ahn, Hee-Kap Weighted center facility location weight assignment combinatorial op- timization computational geometry Given a set P of n points in the plane and a multiset W of k weights with k leq n, we assign a weight in W to a point in P to minimize the maximum weighted distance from the weighted center of P to any point in P. In this paper, we give two algorithms which take O(k^2 n^2 log^4 n) time and O(k^5 n log^4 k + kn log^3 n) time, respectively. For a constant k, the second algorithm takes only O(n log^3 n) time, which is near-linear. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Eunjin Oh and Hee-Kap Ahn 2016 Is Part Of LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2016.58 urn:nbn:de:0030-drops-68275 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.58 eng https://creativecommons.org/licenses/by/3.0/legalcode