I have an idea for a problem but i am not too sure of the solution myself. I have a complicated solution which should work(i think).But there might be a more efficient solution. So check this out and tell me if you get a better solution.
You are given n points in k dimensional space. You have to arrange the points in such a way that no. of decreases of coordinate values among adjacent pair of points is minimum.
Here is an example
For n =4 k =3 and points being (1,4,100), (2,3,5), (4,11,15) , (10,20,30)
Given order is one of the minimal orders and answer is 2 because of 4 to 3 and 100 to 5
For k=2 i strongly believe that there must be some adhoc solution though i could not come up with one yet.
My soln is for constraints like n=100 k can be anything but i think setting k=5 would make it tricky.