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arXiv · 2407.15980

Shortest Path Separators in Unit Disk Graphs

Elfarouk Harb·Zhengcheng Huang·Da Wei Zheng
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Abstract

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.

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Elfarouk Harb, Zhengcheng Huang, Da Wei Zheng. 2024-07-22. Shortest Path Separators in Unit Disk Graphs. https://arxiv.org/abs/2407.15980

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