Hierarchical Agglomerative Graph Clustering in Poly-Logarithmic Depth

Obtaining scalable algorithms for \emph{hierarchical agglomerative clustering} (HAC) is of significant interest due to the massive size of real-world datasets. At the same time, efficiently parallelizing HAC is difficult due to the seemingly sequential nature of the algorithm. In this paper, we address this issue and present ParHAC, the first efficient parallel HAC algorithm with sublinear depth for the widely-used average-linkage function. In particular, we provide a (1 \epsilon) -approximation algorithm for this problem on m edge graphs using \tilde{O}(m) work and poly-logarithmic depth. Moreover, we show that obtaining similar bounds for \emph{exact} average-linkage HAC is not possible under standard complexity-theoretic assumptions.We complement our theoretical results with a comprehensive study of the ParHAC algorithm in terms of its scalability, performance, and quality, and compare with several state-of-the-art sequential and parallel baselines.