Sparse-pivot: Dynamic correlation clustering for node insertions

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 $\log^{O(1)}(n)$. 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.

Suppose we are given items and we know for any two items if they are similar or dissimilar. We want to cluster these items such that similar items are in one cluster and dissimilar items are in different clusters. This is essentially called correlation clustering. In real world, new items might come and we don't want to compute our clustering from scratch. We show that we can maintain a good clustering while spending small amount of time updating it when a new item arrives.