On packing squares with resource augmentation: maximizing the profit

  • Authors:

  • Aleksei V. Fishkin;Olga Gerber;Klaus Jansen;Roberto Solis-Oba

  • Affiliations:

  • Max Planck Institut für Informatik, Saarbrücken, Germany;University of Kiel, Kiel, Germany;University of Kiel, Kiel, Germany;The University of Western Ontario, London, ON, Canada

  • Venue:
  • CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
  • Year:
  • 2005

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Abstract

We consider the problem of packing squares with profits into a bounded square region so as to maximize their total profit. More specifically, given a set L of n squares with positive profits, it is required to pack a subset of them into a unit size square region [0, 1] × [0,1] so that the total profit of the squares packed is maximized. For any given positive accuracy ε 0, we present an algorithm that outputs a packing of a subset of L in the augmented square region [1 + ε] × [1 + ε] with profit value at least (1 - ε)OPT(L), where OPT (L) is the maximum profit that can be achieved by packing a subset of L in the unit square. The running time of the algorithm is polynomial in n for fixed ε.