{"paper":{"title":"Parameterized k-Clustering: The distance matters!","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fedor V. Fomin, Kirill Simonov, Petr A. Golovach","submitted_at":"2019-02-22T17:05:18Z","abstract_excerpt":"We consider the $k$-Clustering problem, which is for a given multiset of $n$ vectors $X\\subset \\mathbb{Z}^d$ and a nonnegative number $D$, to decide whether $X$ can be partitioned into $k$ clusters $C_1, \\dots, C_k$ such that the cost\n  \\[\\sum_{i=1}^k \\min_{c_i\\in \\mathbb{R}^d}\\sum_{x \\in C_i} \\|x-c_i\\|_p^p \\leq D,\\] where $\\|\\cdot\\|_p$ is the Minkowski ($L_p$) norm of order $p$. For $p=1$, $k$-Clustering is the well-known $k$-Median. For $p=2$, the case of the Euclidean distance, $k$-Clustering is $k$-Means. We show that the parameterized complexity of $k$-Clustering strongly depends on the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08559","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":""},"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"}