Fully Dynamic Correlation Clustering: Breaking 3-Approximation
arxiv(2024)
摘要
We study the classic correlation clustering in the dynamic setting. Given n
objects and a complete labeling of the object-pairs as either similar or
dissimilar, the goal is to partition the objects into arbitrarily many clusters
while minimizing disagreements with the labels. In the dynamic setting, an
update consists of a flip of a label of an edge. In a breakthrough result,
[BDHSS, FOCS'19] showed how to maintain a 3-approximation with polylogarithmic
update time by providing a dynamic implementation of the algorithm of
[ACN, STOC'05]. Since then, it has been a major open problem to determine
whether the 3-approximation barrier can be broken in the fully dynamic setting.
In this paper, we resolve this problem. Our algorithm, ,
locally improves the output of by moving some vertices to other
existing clusters or new singleton clusters. We present an analysis showing
that this modification does indeed improve the approximation to below 3. We
also show that its output can be maintained in polylogarithmic time per update.
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