On plane constrained bounded-degree spanners

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 , 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 . We then show how to construct a plane 6-spanner of with maximum degree 6+c, where c is the maximum number of segments adjacent to a vertex. © 2012 Springer-Verlag Berlin Heidelberg.