Before revision:  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.
After revision:  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( |E|\log |E| )-time and O( |E|\log |E| )-space 8-approximation.