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, S1,...,Sk that max 1leqslant i leqslant k |MST(Si) | is minimized. A variant of this problem arises in the shipbuilding industry [2]