A new approximation algorithm for multidimensional rectangle tiling

Authors:
Katarzyna Paluch
Affiliations:
Institute of Computer Science, University of Wroclaw, Poland
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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Abstract

We consider the following tiling problem: Given a d dimensional array A of size n in each dimension, containing non-negative numbers and a positive integer p, partition the array A into at most p disjoint rectangular subarrays called rectangles so as to minimise the maximum weight of any rectangle. The weight of a subarray is the sum of its elements. In the paper we give a $\frac{d+2}{2}$-approximation algorithm that is tight with regard to the only known and used lower bound so far.