Parallel Algorithms for Hierarchical Clustering: Single-Link, Minimum Spanning Trees and Parallel Architectures
This research paper investigates parallel algorithms for hierarchical clustering, a clustering technique in which individual data points initially form separate clusters and the closest clusters are repeatedly merged until a hierarchical tree structure, or dendrogram, is formed. The paper reviews important sequential clustering algorithms, surveys previous parallel approaches and proposes parallel methods for several commonly used inter-cluster distance metrics. Prims_algorithm_for_hierarchica… The paper distinguishes between graph-based metrics and geometric metrics. Graph metrics include single-link, average-link and complete-link clustering, while geometric metrics include centroid, median and minimum-variance methods. It also discusses the Lance–Williams updating formula, which provides a general framework for updating inter-cluster distances after agglomeration. Prims_algorithm_for_hierarchica… Prims_algorithm_for_hierarchica… A major focus is the relationship between single-link hierarchical clustering and the Euclidean minimum spanning tree. The paper explains that the cluster hierarchy for single-link clustering can be obtained from a minimum spanning tree, making minimum-spanning-tree algorithms highly relevant to efficient hierarchical clustering. It presents practical single-link algorithms with O(n²) time complexity and discusses space requirements and nearest-neighbour update properties. Prims_algorithm_for_hierarchica… Prims_algorithm_for_hierarchica… The paper also examines algorithms for metrics satisfying the reducibility property, where nearest-neighbour chains can be used to efficiently determine which clusters to merge. Minimum-variance and graph-based metrics satisfy this property, while centroid and median metrics do not necessarily do so. Prims_algorithm_for_hierarchica… Prims_algorithm_for_hierarchica… For more general clustering metrics, the paper describes priority-queue-based algorithms with O(n² log n) sequential time complexity. It then reviews previous parallel work, including parallel implementations of SLINK, Ward’s method and Prim’s minimum spanning tree algorithm. The cited parallel Prim implementation achieves O(n log n) time when sufficient processors are available. Prims_algorithm_for_hierarchica… Prims_algorithm_for_hierarchica… The core contribution is a set of parallel algorithms for hierarchical clustering on PRAM, butterfly and tree architectures. For single-link clustering, the paper shows how a parallel minimum-spanning-tree approach can be used and reports an O(n log n) running time using n/log n processors. Similar optimal results are described for centroid, median and minimum-variance clustering, while average-link and complete-link methods are more difficult to optimise on local-memory architectures. Prims_algorithm_for_hierarchica… Prims_algorithm_for_hierarchica… Prims_algorithm_for_hierarchica… Overall, the paper demonstrates how hierarchical clustering can be accelerated through parallel computation while preserving the computational structure of different clustering metrics. Its main themes include minimum spanning trees, Prim’s algorithm, single-link clustering, nearest-neighbour methods, PRAM computation, parallel data structures and asymptotic complexity analysis. Prims_algorithm_for_hierarchica… Important: because this file is a journal research paper rather than a university assessment brief, fields such as module name, academic level, assignment type and formal word count do not genuinely apply.
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