Before revision:  More accurate (34+24\sqrt{2}+\varepsilon)-, \left(12+6\sqrt{3}+\varepsilon\right)- and \left(34+38\sqrt{\frac{15}{19}}+\varepsilon\right) -ap\-pro\-xi\-mate algorithms are proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant  .
After revision:  More accurate (34+24\sqrt{2}+\varepsilon)-, \left(12+6\sqrt{3}+\varepsilon\right)- and \left(34+38\sqrt{\frac{15}{19}}+\varepsilon\right) -ap\-pro\-xi\-mate algorithms are proposed for the case where G is any subgraph of either an outerplane or a Gabriel graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon>0 is an arbitrary small constant . Related work only tackles the case where E consists of axis-parallel segments, resulting in an O(|E|\log|E|)-time and O(|E|\log|E|)-space 8-approximation .