Before revision:   Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+ \varepsilon \right)-approximate O\left(n^4\log n\right)-time and O\left(n^2\log n\right)-space algorithm is given based on the modified Agarwal-Pan algorithm  .
After revision:  To the best of our knowledge, related work only tackles a setting where E consists of (generally, properly overlapping) axis-parallel segments, resulting in an O(n\log n)-time and O(n\log n)-space 8-approximation algorithm. Exploiting tough connection of the problem with the geometric Hitting Set problem, an \left(50+52\frac{12{13}}+ \varepsilon \right)-approximate O\left(n^4\log n\right)-time and O\left(n^2\log n\right)-space algorithm is given based on the modified Agarwal-Pan algorithm .