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 Ë 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.

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