This work firstly studies the Steiner tree problem with bounded edge-length d in which d is the ratio of the maximum edge cost to the minimum edge cost. This work analyzes the algorithm of Byrka et al.  and shows that the approximation ratio of [Formula presented] for general graphs and approximation ratio of [Formula presented] for quasi-bipartite graphs. The algorithm implies approximation ratio of 1.162+ϵ for the problem on complete graphs with edge distances 1 and 2. This finding represents an improvement upon the previous best approximation ratio of 1.25. This work then presents a combinatorial two-phase heuristic for the general Steiner tree in greedy strategy that achieves an approximation ratio of 1.4295.
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