Enclosing many boxes by an optimal pair of boxes
We look at the problem: Given a set M of n d- dimensional intervals, find two d-dimensional intervals S, T, such that all intervals in M are enclosed by S or by T, the distribution is balanced and the intervals S and T fulfill a geometric criterion, e.g. like minimum area sum. Up to now no polynomial time algorithm was known for that problem. We present an O(dn log n + d2n2d− 1) algorithm for finding an optimal solution.
Keywordscomputational geometry covering problems axis-parallel rectangles
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