2021/09/13 by Keenan Lee, Lee, Keenan, André van Renssen +1
Computer Science · Engineering · #3D Modeling in Geospatial Applications #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #Robotic Path Planning Algorithms
paper · pdf · doi:10.48550/arxiv.2109.05689
openalex publication_date 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present sweeping line graphs, a generalization of Θ-graphs. We show that these graphs are spanners of the complete graph, as well as of the visibility graph when line segment constraints or polygonal obstacles are considered. Our proofs use general inductive arguments to make the step to the constrained setting. These same arguments could apply to other spanner constructions in the unconstrained setting, removing the need to find separate proofs that they are spanning in the constrained and polygonal obstacle settings.