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. Moreover, an O(n^2\log n)-time and O(n^2)-space 18-approximation is designed for the case where G is any subgraph of a Gabriel graph. To the best of our knowledge, related work only tackles the case where E consists of axis-parallel segments, resulting in an O(n\log n)-time and O(n\log n)-space 8-approximation .
After 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 arbitrarily small constant .