Partitioning a Square into Rectangles: NP-Completeness and Approximation Algorithms
- Cite this article as:
- Beaumont, Boudet, Rastello et al. Algorithmica (2002) 34: 217. doi:10.1007/s00453-002-0962-9
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
-approximation algorithm for (ii).
Key words. NP-completeness, Approximation algorithms, Geometric problems, Heterogeneous resources, Parallel computing.
© Springer-Verlag New York 2002