问题
So I've been working on an algorithm. The task I'm trying to accomplish is: consider a 2D plane there are targets that are randomly distributed between a y upper bound and lower bound. This set is T. T1 is marked with coordinates(X,Y). There is a set S of sensors that are guaranteed to cover every target each sensor has a radius 1 and an (X,Y) coordinate. Each target has a cost (c) that is a weight. So my task is to find a minimum weight or cost for a set S' that covers each sensor.
So I know that there is a recursive relation between the disks that "dominate" or "control" other disks but I'm having trouble seeing a property that shows how to utilize the dominance of the disks. I got this far:
Let D+ be the set of disks whose centre lies above the strip (upper disks).
Let D- be the set of disks whose centre lies below the strip (lower disks).
Consider an upper disk d, and d intersects a vertical line L. Another upper disk d' is said to be controlled or dominated by d, if one of the following holds: (1)d' does not intersect L (2)the lower intersection endpoint of d' and L is higher than the lower intersection endpoint of d and L (3)the lower intersection endpoint of d' and L is identical to the lower intersection endpoint of d and L, but the centre of d' is on the right of the centre of d.
Similarly, for a lower disk d, and d intersects a vertical line L. Another lower disk d' is said to be controlled or dominated by d, if one of the following holds: (1)d' does not intersect L (2)the upper intersection endpoint of d' and L is lower than the upper intersection endpoint of d and L (3)the upper intersection endpoint of d' and L is identical to the upper intersection endpoint of d and L, but the centre of d' is on the right of the centre of d. Example:
But I’m having trouble finalizing the algorithm. any help? Is that clear?
Thanks, Christopher
来源：https://stackoverflow.com/questions/13500227/recursive-relation-help-for-dynamic-programming-2d-plane-algorithm