Generalized sweeping line spanners

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 cons...

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Bibliographic Details
Published in:Theoretical computer science 2024-03, Vol.989, p.114390, Article 114390
Main Authors: Lee, Keenan, van Renssen, André
Format: Article
Language:English
Subjects:
Computational geometry
Obstacles
Spanners
Sweeping line
Θ-graphs
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Summary: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.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114390