The optimal work bounds achieved by the algorithms have significant implications for the practical performance, especially when dealing with large-scale real-world datasets.
The 𝑂(𝑛logℎ) work bound ensures that the algorithms can efficiently compute the SLD even for billion-scale trees, making them suitable for handling massive datasets commonly encountered in various applications. This efficiency translates to faster processing times and improved scalability, allowing for the analysis of complex hierarchical structures in a timely manner.
In practical terms, the algorithms' speedup over existing methods, such as the Union-Find algorithm, can lead to substantial performance gains. The up to 150x speedup observed in the experiments demonstrates the practical impact of the optimized parallel algorithms in reducing computation time for dendrogram computation.
Overall, the optimal work bounds not only enhance the theoretical efficiency of the algorithms but also have tangible benefits for real-world applications, enabling faster and more scalable hierarchical clustering on large datasets.