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Covering point sets with two disjoint disks or squares


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Opened Access Covering point sets with two disjoint disks or squares

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Author: Cabello, Sergio
Díaz Báñez, José Miguel
Seara Ojea, Carlos
Sellarés, J. Antoni
Urrutia, Jorge
Ventura Molina, Inmaculada
Department: Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Date: 2007
Published in: Computational Geometry, 40 (3), 195-206.
Document type: Article
Abstract: We study the following problem: Given a set of red points and a set of blue points on the plane, find two unit disks CR and CB with disjoint interiors such that the number of red points covered by CR plus the number of blue points covered by CB is maximized. We give an algorithm to solve this problem in O(n8/3 log2 n) time, where n denotes the total number of points. We also show that the analogous problem of finding two axis-aligned unit squares SR and SB instead of unit disks can be solved in O(nlog n) time, which is optimal. If we do not restrict ourselves to axis-aligned squares, but require that both squares have a common orientation, we give a solution using O(n3 log n) time.
Cite: Cabello, S., Díaz Báñez, J.M., Seara, C., Sellarés, J.A., Urrutia, J. y Ventura Molina, I. (2007). Covering point sets with two disjoint disks or squares. Computational Geometry, 40 (3), 195-206.
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DOI: 10.1016/j.comgeo.2007.10.001

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