Covering a polygonal region by rectangles
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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.
KeywordsMathematical modeling Optimization Covering problem
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- 1.Bennell, J., Scheithauer, G., Stoyan, Y., Romanova, T.: Tools of mathematical modeling of arbitrary object packing problems. Ann. Oper. Res. (2008). ISSN 0254-5330 (Print) 1572-9338 (Online) Google Scholar
- 2.Daniels, K., Inkulu, R.: An incremental algorithm for translational polygon covering. Technical Report, 2001-001, University of Massachusetts at Lowell Computer Science Google Scholar
- 3.Dyckhoff, H., Scheithauer, G., Terno, J.: Cutting and packing. In: Dell’Amico, M., Maffioli, F. (eds.) Annotated Bibliographies in Combinatorial Optimization, pp. 393–412. Wiley, New York (1997) Google Scholar
- 5.Stoyan, Y.G.: Covering a polygonal region by a collection of various size rectangles. Mech. Eng. Probl. 10(2), 67–82 (2007) Google Scholar
- 6.Stoyan, Y.G., Patsuk, V.: Covering a convex polygon with the given number of equal circles of minimal radius. Comput. Optim. Appl. (2008). Online Google Scholar
- 7.Stoyan, Y.G., Terno, J., Schithauer, G., Gil, N., Romanova, T.: Φ-function for 2D primary objects. Stud. Inform. (Paris Univ.) 2(1), 1–32 (2002) Google Scholar