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Covering a polygonal region by rectangles. (English) Zbl 1219.90147
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.

90C27Combinatorial optimization
Full Text: DOI
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