Approximating Layout Problems on Random Geometric Graphs

@article{Daz2001ApproximatingLP,
  title={Approximating Layout Problems on Random Geometric Graphs},
  author={Josep D{\'i}az and Mathew D. Penrose and Jordi Petit and Maria J. Serna},
  journal={J. Algorithms},
  year={2001},
  volume={39},
  pages={78-116}
}
In this paper, we study the approximability of several layout problems on a family of random geometric graphs. Vertices of random geometric graphs are randomly distributed on the unit square and are connected by edges whenever they are closer than some given parameter. The layout problems that we consider are bandwidth, minimum linear arrangement, minimum cut width, minimum sum cut, vertex separation, and edge bisection. We first prove that some of these problems remain NP-complete even for… 

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