Covering with Rectangular Pieces
نویسندگان
چکیده
The practical problem we are trying to model is: we have to cover a room with a material(carpet or linolleum). This material is in a roll of fixed width. We want to cover the room with a minimum number of pieces and to waste a minimum amount of material. We present in this paper a synthesis of our works. We can easily see that the two criteria, the minimum loss of material and the minimumnumber of pieces, are conflicting. In the first part we present two algorithms for finding the minimum number of pieces when the two areas are equal and to find minimum Pareto optimal points with a diagram when the room is rectangular and ”L” shape. Second we study the property of the covering models. It is shown that all the covering models which contains at most 4 components are with guillotine restrictions and for 5 and 6 components there is only one type of model without guillotine restrictions. Using a two-dimensional language, we find some symmetrical cutting model.
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