# Stabbing Line Segments with Disks: Complexity and Approximation Algorithms

@inproceedings{Kobylkin2017StabbingLS, title={Stabbing Line Segments with Disks: Complexity and Approximation Algorithms}, author={Konstantin Kobylkin}, booktitle={AIST}, year={2017} }

Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii \(r>0\) where the set of segments forms a straight line drawing \(G=(V,E)\) of a planar graph without edge crossings. Close geometric problems arise in network security applications. We give strong NP-hardness of the problem for edge sets of Delaunay triangulations, Gabriel graphs and other subgraphs (which are often…

## 2 Citations

### Efficient constant factor approximation algorithms for stabbing line segments with equal disks

- Computer ScienceArXiv
- 2018

Fast constant factor approximation algorithms are devised for a problem of intersecting a set of straight line segments with the smallest cardinality set of disks of fixed radii $r>0,$ where the set…

### On Covering Segments with Unit Intervals

- Computer Science, MathematicsSTACS
- 2020

This work studies the problem of covering a set of segments on a line with the minimum number of unit-length intervals, and shows that the restrictions of the aforementioned problems to the set of instances in which all the segments have the same length are NP-hard.

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