, Volume 34, Issue 3, pp 217-239

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

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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 s 1 , s 2 , . . . ,s p (such that Σ i=1 p s i = 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).