@article { author = {}, title = {Plane Bounded-Degree Spanners Among the Obstacles for the Points in Convex Position}, journal = {Journal of Algorithms and Computation}, volume = {}, number = {}, pages = {1-4}, year = {2022}, publisher = {University of Tehran}, issn = {2476-2776}, eissn = {2476-2784}, doi = {10.22059/jac.2022.85498}, abstract = {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.}, keywords = {Plane spanner,Stretch factor,Shortest path,computational geometry}, url = {https://jac.ut.ac.ir/article_85498.html}, eprint = {https://jac.ut.ac.ir/article_85498_5cbe45ab3fcd3cad489c9f8fd516623a.pdf} }