  The Hop-Constrained Steiner Tree problem (HCST) is challenging NP-hard
problem arising in the design of centralized telecommunication networks where
the reliability constraints matter. In this paper three iterative greedy
algorithms are described to find efficient optimized solution to solve HCST on
both sparse and dense graphs. In the third algorithm, we adopt the idea of
Kruskal algorithm for the HCST problem to reach a better solution. This is the
first time such algorithm is utilized in a problem with hop-constrained
condition. Computational results on a number of problem instances are derived
from well-known benchmark instances of Steiner problem in graphs. We compare
three algorithms with a previously known method (Voss's algorithm) in term of
effectiveness, and show that the cost of the third proposed method has been
noticeably improved significantly, 34.60% in hop 10 on dense graphs and 3.34%
in hop 3 on sparse graphs.
