Computational Optimization and Applications

, Volume 48, Issue 3, pp 675-695

First online:

Covering a polygonal region by rectangles

  • Y. G. StoyanAffiliated withAcademy of Science of Ukraine
  • , T. RomanovaAffiliated withAcademy of Science of Ukraine
  • , G. ScheithauerAffiliated withDepartment of Mathematics, Technische Universität Dresden Email author 
  • , A. KrivulyaAffiliated withAcademy of Science of Ukraine

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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.


Mathematical modeling Optimization Covering problem