Before revision:  More accurate (34+242+\varepsilon)- , 12+6\sqrt{3+\varepsilon} - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also 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+242+\varepsilon)-  12+6\sqrt{3+\varepsilon} - and \left(34+ 38\sqrt{\frac{15 +\varepsilon\right) -approximate algorithms are also 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.