  DBSCAN is a fundamental spatial clustering algorithm with numerous practical
applications. However, a bottleneck of the algorithm is in the worst case, the
run time complexity is $O(n^2)$. To address this limitation, we propose a new
grid-based algorithm for exact DBSCAN in Euclidean space called GriT-DBSCAN,
which is based on the following two techniques. First, we introduce a grid tree
to organize the non-empty grids for the purpose of efficient non-empty
neighboring grids queries. Second, by utilising the spatial relationships among
points, we propose a technique that iteratively prunes unnecessary distance
calculations when determining whether the minimum distance between two sets is
less than or equal to a certain threshold. We theoretically prove that the
complexity of GriT-DBSCAN is linear to the data set size. In addition, we
obtain two variants of GriT-DBSCAN by incorporating heuristics, or by combining
the second technique with an existing algorithm. Experiments are conducted on
both synthetic and real-world data sets to evaluate the efficiency of
GriT-DBSCAN and its variants. The results of our analyses show that our
algorithms outperform existing algorithms.
