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arXiv · 1710.01431

Massively Parallel Algorithms and Hardness for Single-Linkage Clustering Under $\ell_p$-Distances

Grigory Yaroslavtsev·Adithya Vadapalli
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Abstract

We present massively parallel (MPC) algorithms and hardness of approximation results for computing Single-Linkage Clustering of $n$ input $d$-dimensional vectors under Hamming, $\ell_1, \ell_2$ and $\ell_\infty$ distances. All our algorithms run in $O(\log n)$ rounds of MPC for any fixed $d$ and achieve $(1+\epsilon)$-approximation for all distances (except Hamming for which we show an exact algorithm). We also show constant-factor inapproximability results for $o(\log n)$-round algorithms under standard MPC hardness assumptions (for sufficiently large dimension depending on the distance used). Efficiency of implementation of our algorithms in Apache Spark is demonstrated through experiments on a variety of datasets exhibiting speedups of several orders of magnitude.

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Grigory Yaroslavtsev, Adithya Vadapalli. 2017-10-04. Massively Parallel Algorithms and Hardness for Single-Linkage Clustering Under $\ell_p$-Distances. https://arxiv.org/abs/1710.01431

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