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(  |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}}  \right) |E|^2\log |E| -time and O\left( \frac{|E|^2\log|E|{\varepsilon}}  \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.
After 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(  |E|^2+\frac{|E|\log|E|{\varepsilon^2}+\log|E|{\varepsilon^3}} \right) |E|^2\log |E| -time and O\left( \frac{|E|^2\log|E|{\varepsilon}} n^2\log n \right)-space algorithm is given based on the modified Agarwal-Pan algorithm.