{"paper":{"title":"Parallel Hierarchical Agglomerative Clustering in Low Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DC"],"primary_cat":"cs.DS","authors_text":"D Ellis Hershkowitz, Jakub {\\L}\\k{a}cki, Kishen N Gowda, Laxman Dhulipala, MohammadHossein Bateni, Rajesh Jayaram, Willem Fletcher","submitted_at":"2025-07-26T19:52:50Z","abstract_excerpt":"Hierarchical Agglomerative Clustering (HAC) is an extensively studied and widely used method for hierarchical clustering in $\\mathbb{R}^k$ based on repeatedly merging the closest pair of clusters according to an input linkage function $d$. Highly parallel (i.e., NC) algorithms are known for $(1+\\epsilon)$-approximate HAC (where near-minimum rather than minimum pairs are merged) for certain linkage functions that monotonically increase as merges are performed. However, no such algorithms are known for many important but non-monotone linkage functions such as centroid and Ward's linkage.\n  In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20047","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.20047/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}