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

@article{Beaumont2002PartitioningAS,
  title={Partitioning a Square into Rectangles: NP-Completeness and Approximation Algorithms
},
  author={Olivier Beaumont and Vincent Boudet and Fabrice Rastello and Yves Robert},
  journal={Algorithmica},
  year={2002},
  volume={34},
  pages={217-239}
}
AbstractIn 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).  

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This paper proves NP-completeness and introduces approximation algorithms for partitioning the unit square into p rectangles so as to minimize either the sum of the p perimeters of the rectangles or the largest perimeter of thep rectangles.

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