SPARSE-PIVOT: Dynamic correlation clustering for node insertions

TL;DR

This paper introduces a new dynamic correlation clustering algorithm that efficiently updates clusters with each node insertion, achieving a better approximation factor and demonstrating superior practical performance compared to previous methods.

Contribution

The paper presents SPARSE-PIVOT, a dynamic correlation clustering algorithm with improved approximation factor and efficient update time, validated through theoretical analysis and empirical evaluation.

Findings

Amortized update time of $O_{eta}( ext{log}^{O(1)}(n))$

Approximation factor improved to $20+eta$

Empirical results show better practical performance

Abstract

We present a new Correlation Clustering algorithm for a dynamic setting where nodes are added one at a time. In this model, proposed by Cohen-Addad, Lattanzi, Maggiori, and Parotsidis (ICML 2024), the algorithm uses database queries to access the input graph and updates the clustering as each new node is added. Our algorithm has the amortized update time of $O_{\epsilon}(\log^{O(1)}(n))$. Its approximation factor is $20+\varepsilon$, which is a substantial improvement over the approximation factor of the algorithm by Cohen-Addad et al. We complement our theoretical findings by empirically evaluating the approximation guarantee of our algorithm. The results show that it outperforms the algorithm by Cohen-Addad et al.~in practice.