Proposing to improve the Heuristic Algorithms to Solve a Steiner-minimal-tree Problem in Large Size Sparse Graphs

Steiner Minimal Tree (SMT) is a combinatorial optimization problem that has many important applications in science and engineering; this is an NP-hard class problem. In recent decades, there have been a series of scientific papers published for solving the SMT problem based on the approaches of exact solutions (such as dynamic programming, branch and bound) and approximate solutions (such as heuristic algorithm, metaheuristic algorithm). This paper proposes an improvement for two heuristic algorithms PD-Steiner and SPT-Steiner to solve a SMT problem in large size sparse graphs with edge weight not exceeding 10 and verify this proposal on large-size sparse graphs up to 100000 vertices. These experimental results are useful information for further research on the SMT problem.