Planar maximum box problem

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3 Scopus citations


Given two finite sets of points X+ and X- in R d, the maximum box problem asks to find an axis-parallel box B such that B ∩ X- = φ 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.

Original languageEnglish
Pages (from-to)31-38
Number of pages8
JournalJournal of Mathematical Modelling and Algorithms
Issue number1
StatePublished - 1 Dec 2004


  • Axis-parallel
  • Discrete optimization
  • Sorted matrices


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