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 \(\mathord{\it Vis}(P,S)\), 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-θ 6-graph (which is identical to the constrained Delaunay graph whose empty visible region is an equilateral triangle) is a plane 2-spanner of \(\mathord{\it Vis}(P,S)\). We then show how to construct a plane 6-spanner of \(\mathord{\it Vis}(P,S)\) with maximum degree 6 + c, where c is the maximum number of segments adjacent to a vertex.
Research supported in part by NSERC and the Danish Council for Independent Research. Due to space constraints, some proofs are omitted and available in the full version of this paper.
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Bose, P., Fagerberg, R., van Renssen, A., Verdonschot, S. (2012). On Plane Constrained Bounded-Degree Spanners. In: Fernández-Baca, D. (eds) LATIN 2012: Theoretical Informatics. LATIN 2012. Lecture Notes in Computer Science, vol 7256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29344-3_8
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DOI: https://doi.org/10.1007/978-3-642-29344-3_8
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