A degree 3 plane 5.19-spanner for points in convex position

Document Type : Article

Authors

1 Department of Computer Science, University of Bojnord, Bojnord, Iran

2 Department of Mathematical Sciences, Combinatorial and Geometric Algorithms Lab., Yazd University, Yazd, P.O. Box 89195-741, Iran

Abstract

Let $S$ be a set of $n$ points in the plane that is in convex position. In this paper, using the well-known path-greedy spanner algorithm, we present an algorithm that constructs a plane $\frac{3+4\pi}{3}$-spanner $G$ of degree 3 on the point set $S$. Recently, Biniaz et al. ({\it Towards plane spanners of degree 3, Journal of Computational Geometry, 8 (1), 2017}) have proposed an algorithm that constructs a degree 3 plane $\frac{3+4\pi}{3}$-spanner $G'$ for $S$. We show that there is no upper bound with a constant factor on the total weight of $G'$, but the total weight of $G$ is asymptotically equal to the total weight of the minimum spanning tree of $S$.

Keywords


References
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