The Geodesic Diameter of Polygonal Domains

This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time. For general polygonal domains with h 1, however, no algorithm for computing the geodesic diameter was known prior to this paper. We present first algorithms that compute the geodesic diameter of a given polygonal domain in worst-case time O(n7.73 ) or O(n7 (log n + h)). The algorithms are based on new geometric observations, part of which states as follows: the geodesic diameter of a polygonal domain can be determined by two points in its interior, and in that case there are at least five shortest paths between the two points.

• Type: Conference
• Year: 2010
• Where: ESA
• Authors: Sang Won Bae, Matias Korman, Yoshio Okamoto
• Keywords: Algorithms, ESA 2010, General Polygonal Domains, Geodesic Diameter, Polygonal Domain