Stabbing Line Segments with Disks: Complexity and Approximation Algorithms

  title={Stabbing Line Segments with Disks: Complexity and Approximation Algorithms},
  author={Konstantin Kobylkin},
  • K. Kobylkin
  • Published in AIST 27 July 2017
  • Mathematics, Computer Science
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

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  • B. Mohar
  • Mathematics
    J. Comb. Theory, Ser. B
  • 2001
The main result is the linear lower bound g ( G )⩾ τ /160 (if G − w is 3-connected and τ >1) and it is proved that the minimum face cover problem is NP -hard for planar triangulations and the minimum vertex cover is NP-hard for 2-connected cubic planar graphs.