Mapping a chain task to chained processors
Information Processing Letters
On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity, and Applications
ICDT '99 Proceedings of the 7th International Conference on Database Theory
On the Complexity of the Generalized Block Distribution
IRREGULAR '96 Proceedings of the Third International Workshop on Parallel Algorithms for Irregularly Structured Problems
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
A new approximation algorithm for multidimensional rectangle tiling
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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We consider two tiling problems for two-dimensional arrays: given an n×n array A of nonnegative numbers we are to construct an optimal partition of it into rectangular subarrays. The subarrays cannot overlap and they have to cover all array elements. The first problem (RTILE) consists in finding a partition using p subarrays that minimizes the maximum weight of subarrays (by weight we mean the sum of all elements covered by the subarray). The second, dual problem (DRTILE), is to construct a partition into minimal number of subarrays such that the weight of each subarray is bounded by a given value W. We show a linear-time 7/3-approximation algorithm for the RTILE problem. This improves the best previous result both in time and in approximation ratio. If the array A is binary (i.e. contains only zeroes and ones) we can reduce the approximation ratio up to 2. For the DRTILE problem we get an algorithm which achieves a ratio 4 and works in linear-time. The previously known algorithm with the same ratio worked in time O(n5). For binary arrays we present a linear-time 2-approximation algorithm.