We look at generalized Delaunay graphs in the constrained setting by introducing line segments which the edges of the graph are not allowed to cross. Given an arbitrary convex shape C, a constrained Delaunay graph is constructed by adding an edge between two vertices p and q if and only if there exists a homothet of C with p and q on its boundary that does not contain any other vertices visible to p and q. We show that, regardless of the convex shape C used to construct the constrained Delaunay graph, there exists a constant t (that depends on C) such that it is a plane t-spanner of the visibility graph.
CITATION STYLE
Bose, P., De Carufel, J. L., & van Renssen, A. (2017). Constrained generalized Delaunay graphs are plane spanners. In Advances in Intelligent Systems and Computing (Vol. 532, pp. 281–293). Springer Verlag. https://doi.org/10.1007/978-3-319-48517-1_25
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