Fully Dynamic Adversarially Robust Correlation Clustering in Polylogarithmic Update Time

TL;DR

This paper introduces a randomized algorithm for dynamic correlation clustering that maintains a constant approximation ratio with polylogarithmic update time under adversarial edge label flips, advancing robustness and efficiency.

Contribution

The paper presents the first algorithm achieving an $O(1)$-approximation with polylogarithmic update time in adversarially robust dynamic correlation clustering.

Findings

Algorithm maintains $O(1)$-approximation with $O( ext{log}^2 n)$ update time.

Experimental results show competitive performance on synthetic and real datasets.

Introduces a new sparse-dense decomposition technique with polylogarithmic update time.

Abstract

We study the dynamic correlation clustering problem with $\textit{adaptive}$ edge label flips. In correlation clustering, we are given a $n$-vertex complete graph whose edges are labeled either $(+)$ or $(-)$, and the goal is to minimize the total number of $(+)$ edges between clusters and the number of $(-)$ edges within clusters. We consider the dynamic setting with adversarial robustness, in which the $\textit{adaptive}$ adversary could flip the label of an edge based on the current output of the algorithm. Our main result is a randomized algorithm that always maintains an $O(1)$-approximation to the optimal correlation clustering with $O(\log^{2}{n})$ amortized update time. Prior to our work, no algorithm with $O(1)$-approximation and $\text{polylog}{(n)}$ update time for the adversarially robust setting was known. We further validate our theoretical results with experiments on synthetic and real-world datasets with competitive empirical performances. Our main technical ingredient is an algorithm that maintains $\textit{sparse-dense decomposition}$ with $\text{polylog}{(n)}$ update time, which could be of independent interest.