Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity

@article{Chan2018StabbingRB,
  title={Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity},
  author={Timothy M. Chan and Thomas C. van Dijk and Krzysztof Fleszar and J. Spoerhase and A. Wolff},
  journal={ArXiv},
  year={2018},
  volume={abs/1806.02851}
}
We initiate the study of the following natural geometric optimization problem. The input is a set of axis-aligned rectangles in the plane. The objective is to find a set of horizontal line segments of minimum total length so that every rectangle is stabbed by some line segment. A line segment stabs a rectangle if it intersects its left and its right boundary. The problem, which we call Stabbing, can be motivated by a resource allocation problem and has applications in geometric network design… Expand
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