Network FarthestPoint Diagrams
Abstract
Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network distance. Within this metric space, we study farthest points. We introduce network farthestpoint diagrams, which capture how the farthest pointsand the distance to themchange as we traverse the network. We preprocess a network G such that, when given a query point q on G, we can quickly determine the farthest point(s) from q in G as well as the farthest distance from q in G. Furthermore, we introduce a data structure supporting queries for the parts of the network that are farther away from q than some threshold R > 0, where R is part of the query. We also introduce the minimum eccentricity feedlink problem defined as follows. Given a network G with geometric edge weights and a point p that is not on G, connect p to a point q on G with a straight line segment pq, called a feedlink, such that the largest network distance from p to any point in the resulting network is minimized. We solve the minimum eccentricity feedlink problem using eccentricity diagrams. In addition, we provide a data structure for the query version, where the network G is fixed and a query consists of the point p.
 Publication:

arXiv eprints
 Pub Date:
 April 2013
 arXiv:
 arXiv:1304.1909
 Bibcode:
 2013arXiv1304.1909B
 Keywords:

 Computer Science  Computational Geometry
 EPrint:
 A preliminary version of this work was presented at the 24th Canadian Conference on Computational Geometry