Density-Based clustering in mapReduce with guarantees on parallel time, space, and solution quality

A well-known clustering problem called Density-Based Spatial Clustering of Applications with Noise~(DBSCAN) involves computing the solutions of at least one disk range query per input point, computing the connected components of a graph, and bichromatic fixed-radius nearest neighbor. MapReduce class...

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Bibliographic Details
Published in:Transactions on combinatorics Vol. 14; no. 3; pp. 135 - 156
Main Authors: Sepideh Aghamolaei, Mohammad Ghodsi
Format: Journal Article
Language:English
Published: University of Isfahan 2025
Subjects:
clustering
massively parallel algorithms
near neighbors
range searching
unit disk graph
ISSN:2251-8657, 2251-8665
Online Access:Get full text
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Summary:A well-known clustering problem called Density-Based Spatial Clustering of Applications with Noise~(DBSCAN) involves computing the solutions of at least one disk range query per input point, computing the connected components of a graph, and bichromatic fixed-radius nearest neighbor. MapReduce class is a model where a sublinear number of machines, each with sublinear memory, run for a polylogarithmic number of parallel rounds. Most of these problems either require quadratic time in the sequential model or are hard to compute in a constant number of rounds in MapReduce. In the Euclidean plane, DBSCAN algorithms with near-linear time and a randomized parallel algorithm with a polylogarithmic number of rounds exist. We solve DBSCAN in the Euclidean plane in a constant number of rounds in MapReduce, assuming the minimum number of points in range queries is constant and each connected component fits inside the memory of a single machine and has a constant diameter.
ISSN:2251-8657
2251-8665
DOI:10.22108/toc.2024.138377.2091