An optimal algorithm for the intersection radius of a set of convex polygons

The intersection radius of a finite collection of geometrical objects in the plane is the radius of the smallest closed disk that intersects all the objects in the collection. Bhattacharya et al, showed how the intersection radius can be found in linear time for a collection of line segments in the plane by combining the prune-and-search strategy of Megiddo (J. Assoc. Comput. Mach. 31(1) (1984), 114-127) with the strategy of replacing line segments by lines or points (B. K. Bhattacharya, S. Jadhav, A. Mukhopadhyay, and J. M. Robert, in ''Proceedings of the Seventh Annual ACM Symposium on Computational Geometry,'' pp. 81-88, 1991). In this paper, we enlarge the scope of this technique by showing that it can also be used to find the intersection radius of a collection of convex polygons in O(n) time, where n is the total number of polygon vertices. (C) 1996 Academic Press, Inc.