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

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 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).