Generalized Sweeping Line Spanners
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866910288510451712 |
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| author | Lee, Keenan van Renssen, André |
| author_facet | Lee, Keenan van Renssen, André |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05689 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Generalized Sweeping Line Spanners Lee, Keenan van Renssen, André Computational Geometry 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. |
| title | Generalized Sweeping Line Spanners |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2109.05689 |