Obtaining high-quality solutions to the minimum label spanning tree problem is of crucial importance to efficient communication network design, since such solutions can reduce both the construction cost and the complexity of the ultimate architecture. However, the corresponding optimization task was shown to be hard even for complete graphs. As a consequence, no computationally efficient method for solving this problem exactly in a reasonable time is known to exist and one has to rely on approximation techniques such as heuristic and evolutionary algorithms. In this study, we investigate the performance of a different method called the Cross-Entropy algorithm which relies on rigorous developments in the fields of information theory and stochastic simulation. Our findings indicate that the mathematical soundness of the Cross-Entropy method makes it very reliable and robust as compared to its counterparts. In particular, the obtained results suggest that the Cross-Entropy method is not sensitive to different graph models and that the proposed algorithm can obtain optimal or near-optimal solutions while using a reasonable computational effort.

中文翻译：

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使用交叉熵方法找到最小标签生成树

获得最小标签生成树问题的高质量解决方案对于高效的通信网络设计至关重要，因为这样的解决方案可以降低最终架构的构建成本和复杂性。然而，即使对于完整的图，相应的优化任务也被证明是困难的。因此，已知不存在在合理时间内准确解决该问题的计算有效方法，因此必须依赖近似技术，例如启发式算法和进化算法。在这项研究中，我们研究了一种称为交叉熵算法的不同方法的性能，该算法依赖于信息论和随机模拟领域的严格发展。我们的研究结果表明，与其他方法相比，交叉熵方法的数学可靠性使其非常可靠和稳健。特别是，获得的结果表明交叉熵方法对不同的图模型不敏感，并且所提出的算法可以在使用合理的计算量的同时获得最优或接近最优的解决方案。