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Covering point sets with two disjoint disks or squares [Elektronski vir]Cabello, Sergio ...We study the following problem: Given a set of red points and a set of blue points on the plane, find two unit disks ▫$C_R$▫ and ▫$C_B$▫ with disjoint interiors such that the number of red points ... covered by ▫$C_R$▫ plus the number of blue points covered by ▫$C_B$▫ is maximized. We give an algorithm to solve this problem in ▫$O(n^{8/3}\log^2 n)$▫ time, where ▫$n$▫ denotes the total number of points. We also show that the analogous problem of finding two axis-aligned unit squares ▫$S_R$▫ and ▫$S_B$▫ instead of unit disks can be solved in ▫$O(n\log n)$▫ 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 ▫$O(n^3\log n)$▫ time.Source: Preprint series. - ISSN 1318-4865 (Vol. 45, št. 1027, 2007, str. 1-14)Type of material - e-articlePublish date - 2007Language - englishCOBISS.SI-ID - 14718553
Author
Cabello, Sergio |
Díaz-Báñez, José Miguel |
Seara, Carlos |
Sellarès, J. Antoni |
Urrutia, Jorge |
Ventura, Inma
Topics
covering |
facility location |
geometric optimization |
disks |
squares
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Cabello, Sergio | 25993 |
Díaz-Báñez, José Miguel | ![]() |
Seara, Carlos | ![]() |
Sellarès, J. Antoni | ![]() |
Urrutia, Jorge | ![]() |
Ventura, Inma | ![]() |
Source: Personal bibliographies
and: SICRIS
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