Balanced partition of minimum spanning trees

To better handle situations where additional resources are available to carry out a task, many problems from the manufacturing industry involve "optimally" dividing a task into k smaller tasks. We consider the problem of partitioning a given set S of n points (in the plane) into k subsets, S-1, . . .,S-k, such that max(1less than or equal toiless than or equal tok)\MST(S-i)\ is minimized. A variant of this problem arises in the shipbuilding industry [2].