We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the critical gap method and other greedy strategies, only offer approximate solutions to this problem. Here, we introduce a dynamic programming approach that returns provably optimal solutions in polynomial time -- O(n^2) steps -- for a broad class of clustering objectives. We demonstrate the algorithm through applications to synthetic and empirical networks and show that it outperforms existing heuristics by a significant margin, with a similar execution time.

翻译：我们研究具有一维归因或物理位置的网络聚类问题，例如声望层级或双曲嵌入的相似性维度。现有算法如临界间隙法及其他贪婪策略仅能提供该问题的近似解。本文提出一种动态规划方法，可在多项式时间内（O(n²)步）为广泛聚类目标函数返回可证明的最优解。我们通过合成网络与实证网络的应用验证该算法，结果表明其在执行时间相近的情况下显著优于现有启发式方法。