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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-article
    Publish date - 2007
    Language - english
    COBISS.SI-ID - 14718553