Abstract
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.
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Dumitrescu, A., Tóth, C.D. (2007). Light Orthogonal Networks with Constant Geometric Dilation. In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_16
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DOI: https://doi.org/10.1007/978-3-540-70918-3_16
Publisher Name: Springer, Berlin, Heidelberg
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