We give e cient algorithms to compute an optimal bipartition of a set of points or a set of simple polygons in the plane. In particular, we give an O(n 2 ) algorithm for partitioning a set of n points into two subsets in order to minimize the sum of the perimeters of the convex hulls. We also examine the problems of minimizing the maximum of the perimeters, or the sum/maximum of the areas, for the case in which the partitioning is a line partitioning, induced by some line, and we examine related problems for the bipartitioning of polygons.
The work of Mitchell and Wynters REF studied four flavors of the problem: minimizing the sum of perimeters, the maximum of the perimeters, the sum of the areas enclosed by the fences, and the maximum of the areas.
Finding Optimal Bipartitions of Points and Polygons
WADS
Mathematics Computer Science