Computational Optimization and Applications

, Volume 48, Issue 3, pp 675–695

Covering a polygonal region by rectangles


  • Y. G. Stoyan
    • Academy of Science of Ukraine
  • T. Romanova
    • Academy of Science of Ukraine
    • Department of MathematicsTechnische Universität Dresden
  • A. Krivulya
    • Academy of Science of Ukraine

DOI: 10.1007/s10589-009-9258-1

Cite this article as:
Stoyan, Y.G., Romanova, T., Scheithauer, G. et al. Comput Optim Appl (2011) 48: 675. doi:10.1007/s10589-009-9258-1


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 modelingOptimizationCovering problem

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© Springer Science+Business Media, LLC 2009