On Balanced Geometric Point Set Partitioning Problems

Abstract

Motivated by the airspace sectorization problem in air traffic management, we consider the following family of geometric partitioning problems: Given a finite set of points within a geometric domain, we want to partition the domain, and thereby the point set, in order that the resulting disjoint polygonal pieces are load-balanced, so that each piece contains a specified number of points and satisfies specified geometric constraints, such as fatness (aspect ratio), convexity of the pieces, etc. We consider different variations of the problem having various optimization criteria, including measures of the balance in terms of areas of pieces, number of points per piece, and total length of the edges defining the partition.