Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations research, and numerous areas due to its significance in a wide range of applications. While known to be computationally challenging (NP-hard) several approximation algorithms have been proposed, most with high-order polynomial-time complexity. However, the graph topology of complex networks with heavy-tailed degree distributions present characteristics that can be exploited to yield custom-tailored algorithms. We compare eight algorithms specifically designed for complex networks and evaluate their performance based on accuracy and efficiency for problems of varying sizes and application areas. Rather than relying on a small number of problems, we conduct over 16,000 experiments covering a wide range of network sizes and k-median{} values. While individual results vary, a few methods provide consistently good results. We draw general conclusions about how algorithms perform in practice and provide general guidelines for solutions.

翻译：在图中寻找k-中位数需要识别一个包含k个顶点的子集，使得该子集到图中所有其他顶点的总距离最小。这个问题因其在广泛实际应用中的重要性，在计算机科学、图论、运筹学等多个领域得到了深入研究。尽管已知该问题在计算上具有挑战性（NP难），但已有多种近似算法被提出，其中多数具有高阶多项式时间复杂性。然而，具有重尾度分布的复杂网络拓扑特性可被利用以设计定制化算法。我们比较了八种专门针对复杂网络设计的算法，并基于精度和效率评估了它们在不同规模和应用领域问题上的表现。本研究未局限于少量问题案例，而是进行了超过16,000次实验，覆盖了不同网络规模和k-中位数值的广泛范围。尽管个体结果存在差异，但若干方法始终能提供良好结果。我们得出了关于算法实际表现的总体结论，并为解决方案提供了通用指导原则。