THE BIG SWEEP - ON THE POWER OF THE WAVE-FRONT APPROACH TO VORONOI DIAGRAMS

We show that the wavefront approach to Voronoi diagrams (a determinist ic line-sweep algorithm that does not use geometric transform) can be generalized to distance measures more general than the Euclidean metri c. In fact, we provide the first worst-case optimal (O(n log n) rime, O (n) space) algorithm that is valid for the full class of what has be en called nice metrics in the plane. This also solves the previously o pen problem of providing an O (n log it)-time plane-sweep algorithm fo r arbitrary L(k)-metrics. Nice metrics include all convex distance fun ctions but also distance measures like the Moscow metric, and composed metrics. The algorithm is conceptually simple, but it copes with all possible deformations of the diagram.