On plane constrained bounded-degree spanners

Authors:
Prosenjit Bose;Rolf Fagerberg;André van Renssen;Sander Verdonschot
Affiliations:
School of Computer Science, Carleton University, Ottawa, Canada;Dept. of Mathematics and Computer Science, University of Southern Denmark, Denmark;School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada
Venue:
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Year:
2012

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Abstract

Let P be a set of points in the plane and S a set of non-crossing line segments with endpoints in P. The visibility graph of P with respect to S, denoted Vis(P,S), has vertex set P and an edge for each pair of vertices u,v in P for which no line segment of S properly intersects uv. We show that the constrained half-θ6-graph (which is identical to the constrained Delaunay graph whose empty visible region is an equilateral triangle) is a plane 2-spanner of Vis(P,S). We then show how to construct a plane 6-spanner of Vis(P,S) with maximum degree 6 + c, where c is the maximum number of segments adjacent to a vertex.