Computing geodesic furthest neighbors in simple polygons

摘要

An algorithm is presented for computing geodesic furthest neighbors for all the vertices of a simple polygon, where geodesic denotes the fact that distance between two points of the polygon is defined as the length of an Euclidean shortest path connecting them within the polygon. The algorithm runs in O(n log n) time and uses O(n) space; n being the number of vertices of the polygon. As a corollary, the geodesic diameter of the polygon also can be computed within, the same time and space bounds.