New algorithms approximate hierarchical clustering into trees and bounded-diameter graphs

Researchers have developed new approximation algorithms for hierarchical clustering problems, specifically when the goal is to partition data into trees or graphs with bounded diameter. The proposed framework leverages linear programming and is applicable to graph classes where a related flat clustering problem, $p_{\mathcal{F}}$-Partitioning, can be formulated with an Integer Linear Program and a rounding procedure. The study also demonstrates that approximating these clustering problems within any constant factor is unlikely under the Small Set Expansion Hypothesis. AI

IMPACT This research advances theoretical understanding of clustering algorithms, potentially impacting future AI systems that rely on data partitioning and structure discovery.

RANK_REASON The cluster contains an academic paper detailing new algorithms and theoretical hardness results for a specific type of clustering problem. [lever_c_demoted from research: ic=1 ai=1.0]

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• bounded diameter graphs
• Dasgupta
• hierarchical clustering
• Hierarchical $\mathcal{F}$-Clustering
• linear programming
• $p_{\mathcal{F}}$-Partitioning
• Small set expansion hypothesis

• paper
• other

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