Fully Dynamic Adversarially Robust Correlation Clustering in Polylogarithmic Update Time

• URL: http://arxiv.org/abs/2411.09979v1
• Date: Fri, 15 Nov 2024 06:26:37 GMT
• Title: Fully Dynamic Adversarially Robust Correlation Clustering in Polylogarithmic Update Time
• Authors: Vladimir Braverman, Prathamesh Dharangutte, Shreyas Pai, Vihan Shah, Chen Wang,
• Abstract summary: We study the dynamic correlation clustering problem with $textitadaptive$ edge label flips. In correlation clustering, we are given a $n$-vertex complete graph whose edges are labeled either $(+)$ or $(-)$. We consider the dynamic setting with adversarial robustness, in which the $textitadaptive$ adversary could flip the label of an edge based on the current output of the algorithm.
• Score: 19.25942907402098
• License:
• 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.

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