Computer Science – Computational Geometry
Scientific paper
2010-01-05
Computer Science
Computational Geometry
21 pages, 7 figures, preliminary version presented at ESA2010 and submitted to DCG
Scientific paper
This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time, as known by Hershberger and Suri. 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 algorithms that compute the geodesic diameter of a given polygonal domain in worst-case time O(n^7.73) or O(n^7 (log n + h)). The main difficulty unlike the simple polygon case relies on the following observation revealed in this paper: two interior points can determine the geodesic diameter and in that case there exist at least five distinct shortest paths between the two.
Bae Sang Won
Korman Matias
Okamoto Yoshio
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