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Zbl 1219.90147
Stoyan, Y.G.; Romanova, T.; Scheithauer, G.; Krivulya, A.
Covering a polygonal region by rectangles. (English)
[J] Comput. Optim. Appl. 48, No. 3, 675-695 (2011). ISSN 0926-6003; ISSN 1573-2894/e

Summary: The problem of covering a compact polygonal region, called target region, with a finite family of rectangles is considered. Tools for mathematical modeling of the problem are provided. Especially, a function, called $\Gamma$-function, is introduced which indicates whether the rectangles with respect to their configuration form a cover of the target region or not. The construction of the $\Gamma$-function is similar to that of $\Phi$-functions which have been proved to be an efficient tool for packing problems. A mathematical model of the covering problem based on the $\Gamma$-function is proposed as well as a solution strategy. The approach is illustrated by an example and some computational results are presented.

MSC 2000:: *90C27 Combinatorial programming

Keywords: mathematical modeling; optimization; covering problem

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