Robust Online Correlation Clustering

In correlation clustering we are given a set of points along with recommendations whether each pair of points should be placed in the same cluster or into separate clusters. The goal is to cluster the points to minimize disagreements from the recommendations. We study the correlation clustering problem in the online setting, where points arrive one at a time, and upon arrival the algorithm must make an irrevocable cluster assignment decision. While the online version is natural, there is a simple lower bound that rules out any algorithm with a non-trivial competitive ratio. In this work we go beyond worst case analysis, and show that the celebrated Pivot algorithm performs well when given access to a small number of random samples from the input. Moreover, we prove that Pivot is robust to additional adversarial perturbations of the sample set in this setting. We conclude with an empirical analysis validating our theoretical findings.