Light Orthogonal Networks with Constant Geometric Dilation

An orthogonal spanner network for a given set of n points in the plane is a plane straight line graph with axis-aligned edges that connects all input points. We show that for any set of n points in the plane, there is an orthogonal spanner network that (i) is short having a total edge length at most a constant times the length of a Euclidean minimum spanning tree for the point set; (ii) is small having O(n) vertices and edges; and (iii) has constant geometric dilation, which means that for any two points u and v in the network, the shortest path in the network between u and v is at most a constant times longer than the Euclidean distance between u and v. Such a network can be constructed in O(n log n) time.

• Type: Conference
• Year: 2007
• Where: STACS
• Authors: Adrian Dumitrescu, Csaba D. Tóth
• Keywords: Euclidean Minimum Spanning Tree, Orthogonal Spanner Network, Plane Straight Line, STACS 2007, Theoretical Computer Science