Poster
Fully Dynamic Adversarially Robust Correlation Clustering in Polylogarithmic Update Time
Anqi Liu · Guanyang Wang · Prashanth A. · Sriram Ganapathi Subramanian · Danqi Liao
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Abstract
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Abstract:
We study the dynamic correlation clustering problem with *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 *adaptive* adversary can 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(log2n) amortized update time. Prior to our work, no algorithm with O(1)-approximation and 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 *sparse-dense decomposition* with polylog(n) update time, which could be of independent interest.
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