Stabbing line segments with disks: complexity and approximation algorithms · arXivDesk
1605.00313May 1, 201612 pages, 1 appendix, 15 bibliography items, 6th International Conference on Analysis of Images, Social Networks and Texts (AIST-2017)
Stabbing line segments with disks: complexity and approximation algorithms
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 used in network design) for r∈[dmin,ηdmax]
Nearby in the stack
and some constant
η
where
dmax
and
dmin
are Euclidean lengths of the longest and shortest graph edges respectively. Fast
O(∣E∣log∣E∣)
-time
O(1)
-approximation algorithm is proposed within the class of straight line drawings of planar graphs for which the inequality
r≥ηdmax
holds uniformly for some constant
η>0,
i.e. when lengths of edges of
G
are uniformly bounded from above by some linear function of