Light Orthogonal Networks with Constant Geometric Dilation

  • Adrian Dumitrescu
  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)


An orthogonal network for a given set of n points in the plane is an axis-aligned planar straight line graph that connects all input points. We show that for any set of n points in the plane, there is an orthogonal network that (i) is short having a total edge length of O(|T|), where |T| denotes the length of a minimum Euclidean 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 constant times longer than the (Euclidean) distance between u and v.


Steiner Tree Narrow Channel Steiner Point Base Side Parallel Edge 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Adrian Dumitrescu
    • 1
  • Csaba D. Tóth
    • 2
  1. 1.Department of Computer Science, University of Wisconsin-MilwaukeeUSA
  2. 2.Department of Mathematics, MIT, CambridgeUSA

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