Before revision:  More accurate (34+242+ \varepsilon )- and \left( 34 + 44\sqrt{\frac{6 + \varepsilon \right)-approxi\-mate algorithms are also proposed for cases where G is any subgraph of either an outerplane 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 )- and \left( 34 + 32\sqrt{\frac{3 + \varepsilon \right)-approxi\-mate algorithms are also proposed for cases where G is any subgraph of either an outerplane graph or a Delaunay triangulation respectively, which work within the same time and space complexity bounds, where \varepsilon >0 is an arbitrary small constant.