Given a set of point sites in a simple polygon, the geodesic farthest-point Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an O(n log log n+m logm)time algorithm to compute the geodesic farthest-point Voronoi diagram of m point sites in a simple n-gon. This i...

We prove some results on the farthest points in convex metric spaces and in linear metric spaces. The continuity of the farthest point map and characterization of strictly convex linear metric spaces in terms of farthest points are also discussed.

w0-Nearest Points and w0-Farthest Point in Normed Linear Spaces

In this paper, we consider the problem of farthest poinst for bounded sets in a real 2-normed spaces. We investigate some properties of farthest points in the setting of 2-normalised spaces and present various characterizations of b-farthest point of elements by bounded sets in terms of b-linear functional. We also provide some applications of farthest points in the setting of 2inner product sp...

In this paper, we give a complete description of the farthest point map, as defined on regular octahedron with its intrinsic flat cone metric. As consequence show that every well-defined orbit map converges to 1-skeleton barycentric subdivision triangulation.

In this paper, we consider the problem of the farthest poinst for bounded sets in a real 2-normed spaces. We investigate some properties of farthest points in the setting of 2-normalised spaces and present various characterizations of b-farthest point of elements by bounded sets in terms of b-linear functional. We also provide some applications of farthest points in the setting of 2inner produc...

Given a set of sites (points) in a simple polygon, the farthest-point geodesic Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an O((n + m) log logn)time algorithm to compute the farthest-point geodesic Voronoi diagram for m sites lying on the boundary of a si...