Exact and rapid linear clustering of networks with dynamic programming

TL;DR

This paper introduces a dynamic programming algorithm that efficiently computes optimal linear clusterings of networks with nodes in one dimension, outperforming existing heuristics in accuracy while maintaining polynomial time complexity.

Contribution

The paper presents a novel dynamic programming method that guarantees optimal solutions for linear network clustering problems within polynomial time, improving upon approximate algorithms.

Findings

The algorithm achieves optimal clustering solutions in O(n^2) time.

It outperforms existing greedy heuristics in accuracy.

The method is effective on both synthetic and real-world networks.

Abstract

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.