Static to Dynamic Correlation Clustering

2025-04-16

AI Summary

This paper addresses the fully dynamic maintenance of correlation clustering on evolving graphs under adaptive adversaries, where edges are inserted or deleted arbitrarily, aiming to minimize both the number of inter-cluster edges and intra-cluster missing edges. The proposed method builds upon a generic dynamicization framework, integrating the Pivot heuristic with the state-of-the-art near-linear-time static 1.437-approximation algorithm, and introduces randomized resampling and local repair strategies. It yields the first fully dynamic algorithm achieving a 1.437-approximation ratio—surpassing prior work limited to oblivious adversaries and offering only an expected 3-approximation. Theoretically, it guarantees worst-case constant-time updates and maintains a 1.437-approximate solution with constant probability at any time step. This significantly improves robustness against adaptive adversarial updates and real-time responsiveness.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Adversarial Agents
• Search and Optimization: Adversarial Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Correlation clustering is a well-studied problem, first proposed by Bansal, Blum, and Chawla [BBC04]. The input is an unweighted, undirected graph. The problem is to cluster the vertices so as to minimizing the number of edges between vertices in different clusters and missing edges between vertices inside the same cluster. This problem has a wide application in data mining and machine learning. We introduce a general framework that transforms existing static correlation clustering algorithms into fully-dynamic ones that work against an adaptive adversary. We show how to apply our framework to known efficient correlation clustering algorithms, starting from the classic 3-approximate Pivot algorithm from [ACN08]. Applied to the most recent near-linear 1.437-approximation algorithm from [CCL+25], we get a 1.437-approximation fully-dynamic algorithm that works with worst-case constant update time. The original static algorithm gets its approximation factor with constant probability, and we get the same against an adaptive adversary in the sense that for any given update step not known to our algorithm, our solution is a 1.437-approximation with constant probability when we reach this update. Previous dynamic algorithms had approximation factors around 3 in expectation, and they could only handle an oblivious adversary.

Problem

• Transforming static correlation clustering into dynamic algorithms
• Achieving constant update time with 1.437-approximation
• Handling adaptive adversaries in dynamic clustering

Innovation

• Transforms static algorithms into dynamic ones
• Achieves 1.437-approximation with constant probability
• Handles adaptive adversary with worst-case updates