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...

Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network distance. Within this metric space, we study farthest points and farthest distances. We introduce a data structure supporting queries for the farthest distan...

Consider the continuum of points on the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network distance. Within this metric space, we study farthest points and farthest distances. We introduce optimal data structures supporting queries for the farthest di...

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...

6 Consider the continuum of points on the edges of a network, i.e., a connected, undirected graph 7 with positive edge weights. We measure the distance between these points in terms of the weighted 8 shortest path distance, called the network distance. Within this metric space, we study farthest points 9 and farthest distances. We introduce optimal data structures supporting queries for the far...