Epsilon nets and union complexity

@inproceedings{Varadarajan2009EpsilonNA,
  title={Epsilon nets and union complexity},
  author={Kasturi R. Varadarajan},
  booktitle={Symposium on Computational Geometry},
  year={2009}
}
We consider the following combinatorial problem: given a set of n objects (for example, disks in the plane, triangles), and an integer L ≥ 1, what is the size of the smallest subset of these n objects that covers all points that are in at least L of the objects? This is the classic question about the size of an L/n-net for these objects. It is well known that for fairly general classes of geometric objects the size of an L/n-net is O(n/L log n/L). There are some instances where this general… CONTINUE READING
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