Plane Bounded-Degree Spanners Among the Obstacles for the Points in Convex Position
Document Type : Research Paper
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.
(2022). Plane Bounded-Degree Spanners Among the Obstacles for the Points in Convex Position. Journal of Algorithms and Computation, (), 1-4. doi: 10.22059/jac.2022.85498
MLA
. "Plane Bounded-Degree Spanners Among the Obstacles for the Points in Convex Position". Journal of Algorithms and Computation, , , 2022, 1-4. doi: 10.22059/jac.2022.85498
HARVARD
(2022). 'Plane Bounded-Degree Spanners Among the Obstacles for the Points in Convex Position', Journal of Algorithms and Computation, (), pp. 1-4. doi: 10.22059/jac.2022.85498
VANCOUVER
Plane Bounded-Degree Spanners Among the Obstacles for the Points in Convex Position. Journal of Algorithms and Computation, 2022; (): 1-4. doi: 10.22059/jac.2022.85498