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arXiv · 1001.3332

Minimum Vertex Cover in Rectangle Graphs

Reuven Bar-Yehuda·Danny Hermelin·Dror Rawitz
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Abstract

We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\calR$ where $R_1 \setminus R_2$ is connected for every pair of rectangles $R_1,R_2 \in \calR$. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of $(1.5 + \varepsilon)$ in general rectangle families, for any fixed $\varepsilon > 0$, and works also for the weighted variant of the problem. Both algorithms exploit the plane properties of axis-parallel rectangles in a non-trivial way.

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Reuven Bar-Yehuda, Danny Hermelin, Dror Rawitz. 2010-01-19. Minimum Vertex Cover in Rectangle Graphs. https://arxiv.org/abs/1001.3332

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