Dynamic Density Based Clustering.

Dynamic clustering---how to efficiently maintain data clusters along with updates in the underlying dataset---is a difficult topic. This is especially true for density-based clustering, where objects are aggregated based on transitivity of proximity, under which deciding the cluster(s) of an object may require the inspection of numerous other objects. The phenomenon is unfortunate, given the popular usage of this clustering approach in many applications demanding data updates. Motivated by the above, we investigate the algorithmic principles for dynamic clustering by DBSCAN, a successful representative of density-based clustering, and ρ-approximate DBSCAN, proposed to bring down the computational hardness of the former on static data. Surprisingly, we prove that the ρ-approximate version suffers from the very same hardness when the dataset is fully dynamic, namely, when both insertions and deletions are allowed. We also show that this issue goes away as soon as tiny further relaxation is applied, yet still ensuring the same quality---known as the ``sandwich guarantee''---of ρ-approximate DBSCAN. Our algorithms guarantee near-constant update processing, and outperform existing approaches by a factor over two orders of magnitude.