| Suppose that we have several polytopes in Rd and we can translate them without rotation. Here we consider the intersection maximization problem, which asks the positions of the polytopes which maximizes the volume of their intersection.In this paper, we address this problem, and show that the problem can be solved in oracle polynomial time by an ellipsoid method, exploiting two important facts. Namely, the objective function is a continuous piecewise-polynomial function and its dth root is concave. We further study the structure of the problem in depth for the two dimensional case, and propose an algorithm which solves it in O(n4) time for two non-convex polygons, where n is the total number of vertices. |
|
