Computing the geodesic centers of a polygonal domain ?
We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is O(n12+?) O ( n 12 + ? ) for any ?>0 ? > 0 , where n  is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an O(nlog?n) O ( n log ? n ) -time algorithm is known by Pollack et al. Our algorithm is the first one that can handle general polygonal domains having one or more polygonal holes.
geodesic center polygonal domain shortest path exact algorithm