On weighted rectangle packing with large resources
We study the problem of packing a set of n rectangles with weights into a dedicated rectangle so that the weight of the packed rectangles is maximized. We consider the case of large resources, that is, the side length of all rectangles is at most 1 and the side lengths of the dedicated rectangle differ by a factor of at least 1/ge 4 for a fixed positive e > 0. We present an algorithm which finds a rectangle packing of weight at least (1−e) of the optimum in time polynomial in n. As an application we show a (2+e)-approximation algorithm for packing weighted rectangles into k rectangular bins of size (a, b).
This work was aimed at understanding mechanisms of importance for the design of weight-efficient armour against long-rod projectiles (LRP) and shaped charge (SC) warheads. The focus was on how to a ...