Plane Bounded-Degree Spanners Among the Obstacles for the Points in Convex Position

Document Type : Research Paper


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


Let $S$ be a set of points in the plane that are in convex position. Let~$\cal O$ be a set of simple polygonal obstacles whose vertices are in $S$. The visibility graph $Vis(S,{\cal O})$  is the graph which is obtained from the complete graph of $S$ by removing all edges intersecting some obstacle of $\cal O$. In this paper, we show that there is a plane $5.19$-spanner  of the visibility graph $Vis(S,{\cal O})$ of  degree at most 6. Moreover, we show that there is a plane $1.88$-spanner of the visibility graph $Vis(S,{\cal O})$.  These  improve the stretch factor and the maximum degree  of the previous results by A. van Renssen and  G. Wong ({\em Theoretical Computer Science, 2021}) in the context of points in convex position.