The farthest line-segment Voronoi diagram shows properties surprisingly different than the farthest point Voronoi diagram: Voronoi regions may be disconnected and they are not characterized by convexhull properties. In this paper we introduce the farthest line-segment hull, a cyclic structure that relates to the farthest line-segment Voronoi diagram similarly to the way an ordinary convex hull ...

We present structural properties of the farthest line-segment Voronoi diagram in the piecewise linear L∞ and L1 metrics, which are computationally simpler than the standard Euclidean distance and very well suited for VLSI applications. We introduce the farthest line-segment hull, a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and is related...

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...

The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction algorithm that is easy to implement. No restr...

1 The farthest-point Voronoi diagram of a set of n sites 2 is a tree with n leaves. We investigate whether arbi3 trary trees can be realized as farthest-point Voronoi di4 agrams. Given an abstract ordered tree T with n leaves 5 and prescribed edge lengths, we produce a set of n sites 6 S in O(n) time such that the farthest-point Voronoi di7 agram of S represents T . We generalize this algorithm...

The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearestand farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-si...

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...

given a set  of  points in the plane and a constant ,-center problem is to find two closed disks which each covers the whole , the diameter of the bigger one is minimized, and the distance of the two centers is at least . constrained -center problem is the -center problem in which the centers are forced to lie on a given line . in this paper, we first introduce -center problem and its constrain...

We investigate the higher-order Voronoi diagrams of n point sites with respect to the geodesic distance in a simple polygon with h > 0 polygonal holes and c corners. Given a set of n point sites, the korder Voronoi diagram partitions the plane into several regions such that all points in a region share the same k nearest sites. The nearest-site (first-order) geodesic Voronoi diagram has already...