Shortest Path Separators in Unit Disk Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909265200939008 |
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| author | Harb, Elfarouk Huang, Zhengcheng Zheng, Da Wei |
| author_facet | Harb, Elfarouk Huang, Zhengcheng Zheng, Da Wei |
| contents | We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves their result that requires removing the 3-hop neighborhood of two shortest paths. Our proof uses very different ideas, including Delaunay triangulations and a generalization of the celebrated balanced separator theorem of Lipton and Tarjan [J. Appl. Math. '79] to systems of non-intersecting paths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15980 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shortest Path Separators in Unit Disk Graphs Harb, Elfarouk Huang, Zhengcheng Zheng, Da Wei Computational Geometry Data Structures and Algorithms We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves their result that requires removing the 3-hop neighborhood of two shortest paths. Our proof uses very different ideas, including Delaunay triangulations and a generalization of the celebrated balanced separator theorem of Lipton and Tarjan [J. Appl. Math. '79] to systems of non-intersecting paths. |
| title | Shortest Path Separators in Unit Disk Graphs |
| topic | Computational Geometry Data Structures and Algorithms |
| url | https://arxiv.org/abs/2407.15980 |