L_1 Geodesic Farthest Neighbors in a Simple Polygon and Related Problems
نویسنده
چکیده
In this paper, we investigate the L1 geodesic farthest neighbors in a simple polygon P , and address several fundamental problems related to farthest neighbors. Given a subset S ⊆ P , an L1 geodesic farthest neighbor of p ∈ P from S is one that maximizes the length of L1 shortest path from p in P . Our list of problems include: computing the diameter, radius, center, farthestneighbor Voronoi diagram, and two-center of S under the L1 geodesic distance. We show that all these problems can be solved in linear or near-linear time based on our new observations on farthest neighbors and extreme points. Among them, the key observation shows that there are at most four extreme points of any compact subset S ⊆ P with respect to the L1 geodesic distance after removing redundancy. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
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