The Flip Diameter of Rectangulations and Convex Subdivisions.

We study the configuration space of rectangulations and convex subdivisions of n points in the plane. It is shown that a sequence of O (n log n) elementary flip and rotate operations can transform any rectangulation to any other rectangulation on the same set of n points. This bound is the best possible for some point sets, while Theta(n) operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of n points in the plane.