Abstract
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 Γ-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 Γ-function is similar to that of Φ-functions which have been proved to be an efficient tool for packing problems. A mathematical model of the covering problem based on the Γ-function is proposed as well as a solution strategy. The approach is illustrated by an example and some computational results are presented.
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Stoyan, Y.G., Romanova, T., Scheithauer, G. et al. Covering a polygonal region by rectangles. Comput Optim Appl 48, 675–695 (2011). https://doi.org/10.1007/s10589-009-9258-1
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DOI: https://doi.org/10.1007/s10589-009-9258-1