The all-geodesic furthest neighbor problem for simple polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
Computing the geodesic center of a simple polygon
Discrete & Computational Geometry
Optimal shortest path queries in a simple polygon
Journal of Computer and System Sciences
Computing the geodesic diameter of a 3-polytope
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Matrix Searching with the Shortest-Path Metric
SIAM Journal on Computing
Star Unfolding of a Polytope with Applications
SIAM Journal on Computing
Handbook of discrete and computational geometry
Two-point Euclidean shortest path queries in the plane
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
SIAM Journal on Computing
A theorem on polygon cutting with applications
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Shortest Path Queries in Polygonal Domains
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
The geodesic farthest-site Voronoi diagram in a polygonal domain with holes
Proceedings of the twenty-fifth annual symposium on Computational geometry
Shortest Path Problems on a Polyhedral Surface
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Querying Two Boundary Points for Shortest Paths in a Polygonal Domain
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The geodesic diameter of polygonal domains
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
The geodesic diameter of polygonal domains
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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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. In this paper, we present the first algorithm that computes the geodesic diameter of a given polygonal domain in worst-case time O(n7.73) or O(n7(log n+h)). Among other results, we show the following geometric observation: the geodesic diameter can be determined by two points in its interior. In such a case, there are at least five shortest paths between the points.