Abstract
Given two finite sets of points X + and X − in ℝd, the maximum box problem asks to find an axis-parallel box B such that B∩X −=∅ and the total number of points from X + covered is maximized. In this paper we consider the version of the problem for d = 2 (and find the smallest solution box). We present an O(n 3 log4 n) runtime algorithm, thus improving previously best known solution by almost quadratic factor.
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Segal, M. Planar Maximum Box Problem. Journal of Mathematical Modelling and Algorithms 3, 31–38 (2004). https://doi.org/10.1023/B:JMMA.0000026707.29260.82
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DOI: https://doi.org/10.1023/B:JMMA.0000026707.29260.82