Multiple Containment Methods
نویسندگان
چکیده
We present three diierent methods for nding solutions to the 2D translation-only containment problem: nd translations for k polygons that place them inside a given polygonal container without overlap. Both the container and the polygons to be placed in it may be nonconvex. First, we provide several exact algorithms that improve results for k = 2 or k = 3. In particular, we give an algorithm for three convex polygons and a nonconvex container with running time in O(m 3 n log mn), where n is the number of vertices in the container, and m is the sum of the vertices of the k polygons. This is an improvement of a factor of n 2 over previous algorithms. Second, we give an approximation algorithm for k nonconvex polygons and a nonconvex container based on restriction and subdivision of the connguration space. Third, we develop a MIP (mixed integer programming) model for k nonconvex polygons and a nonconvex container.
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