Towards Plane Spanners of Degree 3

Let S be a finite set of points in the plane that are in convex position. We present an algorithm that constructs a plane 3+4π 3 -spanner of S whose vertex degree is at most 3. Let Λ be the vertex set of a finite non-uniform rectangular lattice in the plane. We present an algorithm that constructs a plane 3 √ 2-spanner for Λ whose vertex degree is at most 3. For points that are in the plane and in general position, we show how to compute plane degree-3 spanners with a linear number of Steiner points. 1998 ACM Subject Classification I.3.5 Computational Geometry and Object Modeling, F.2.2 Nonnumerical Algorithms and Problems