Algorithms for the Circle-Packing Problem via Extended Sequence-Pair
The circle-packing problem is a problem of packing circles into a two dimensional area such that none of them overlap with each other. Each of the former methods has its own difficulty; some of them are only applicable to the case that the area the circles are to be packed into has a special shape; some of them require different search technique according as the shape of the area. Also, most of the former methods search in a restricted neighbor. In addition, there exist unsearchable location of circles. These facts mean former methods cannot assure global optimization. Hence, in the present paper, we propose sequence-pair for circle packing (SPC), a method of representing relative location of circle pairs, which is an extended version of sequence-pair for rectangles. We propose also a method of obtaining an approximate solution of the circle-packing problem, where all constraints are replaced by approximate linear inequalities.
KeywordsCircle-packing Linear approximation Linear programming Non-linear programming Packing density Reducing redundancy Sequence-pair
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