{"paper":{"title":"Fully dynamic hierarchical diameter k-clustering and k-center","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christian Sohler, Melanie Schmidt","submitted_at":"2019-08-07T14:04:23Z","abstract_excerpt":"We develop dynamic data structures for maintaining a hierarchical k-center clustering when the points come from a discrete space $\\{1,\\ldots,\\Delta\\}^d$. Our first data structure is for the low dimensional setting, i.e., d is a constant, and processes insertions, deletions and cluster representative queries in $\\log^{O(1)} (\\Delta n)$ time, where $n$ is the current size of the point set. For the high dimensional case and an integer parameter $\\ell > 1$, we provide a randomized data structure that maintains an $O(d \\ell)$-approximation. The amortized expected insertion time is $O(d^2 \\ell \\log "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02645","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/1908.02645/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"}