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An NP-hard problem is considered of intersecting a given set of $n$ straightline segments on the plane with the smallest cardinality set of disks of fixedradii $r>0,$ where the set of segments forms a straight line drawing $G=(V,E)$of a planar graph without proper edge crossings. To the best of our knowledge,related work only tackles a setting where $E$ consists of (generally, properlyoverlapping) axis-parallel segments, resulting in an $O(n\log n)$-time and$O(n\log n)$-space 8-approximation algorithm. Exploiting tough connection ofthe problem with the geometric Hitting Set problem, an$\left(50+52\sqrt{\frac{12}{13}}+\nu\right)$-approximate $O\left(n^4\logn\right)$-time and $O\left(n^2\log n\right)$-space algorithm is devised basedon the modified Agarwal-Pan algorithm, which uses epsilon nets. More accurate$(34+24\sqrt{2}+\nu)$- and$\left(\frac{144}{5}+32\sqrt{\frac{3}{5}}+\nu\right)$-approxi\-mate algorithmsare also proposed for cases where $G$ is any subgraph of either a generalizedouterplane graph or a Delaunay triangulation respectively, which work withinthe same time and space complexity bounds, where $\nu>0$ is an arbitrarilysmall constant.

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