Exact and rapid linear clustering of networks with dynamic programming

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