A fast planar partition algorithm. I

A fast randomized algorithm is given for finding a partition of the plane induced by a given set of linear segments. The algorithm is ideally suited for a practical use because it is extremely simple and robust, as well as optimal; its expected running time is O(m+n log n) where n is the number of input segments and m is the number of points of intersection. The storage requirement is O(m+n). Though the algorithm itself is simple, the global evolution of the partition is complex, which makes the analysis of the algorithm theoretically interesting in its own right.<>