Algorithmica

, Volume 34, Issue 3, pp 217–239

Partitioning a Square into Rectangles: NP-Completeness and Approximation Algorithms

  • Beaumont
  • Boudet
  • Rastello
  • Robert
Article

DOI: 10.1007/s00453-002-0962-9

Cite this article as:
Beaumont, Boudet, Rastello et al. Algorithmica (2002) 34: 217. doi:10.1007/s00453-002-0962-9

Abstract

In this paper we deal with two geometric problems arising from heterogeneous parallel computing: how to partition the unit square into p rectangles of given area s1, s2, . . . ,sp (such that Σi=1p si = 1 ), so as to minimize either (i) the sum of the p perimeters of the rectangles or (ii) the largest perimeter of the p rectangles? For both problems, we prove NP-completeness and we introduce a 7/4 -approximation algorithm for (i) and a
$$(2/\sqrt{3})$$
-approximation algorithm for (ii).
Key words. NP-completeness, Approximation algorithms, Geometric problems, Heterogeneous resources, Parallel computing. 

Copyright information

© Springer-Verlag New York 2002

Authors and Affiliations

  • Beaumont
    • 1
  • Boudet
    • 1
  • Rastello
    • 1
  • Robert
    • 1
  1. 1.LIP, UMR CNRS-ENS Lyon-INRIA 5668, Ecole Normale Supérieure de Lyon, F-69364 Lyon Cedex 07, France. Contact: Yves.Robert@ens-lyon.fr.FR

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