{"paper":{"title":"On Computing Centroids According to the $p$-Norms of Hamming Distance Vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Danny Hermelin, Jiehua Chen, Manuel Sorge","submitted_at":"2018-07-17T14:30:03Z","abstract_excerpt":"In this paper we consider the $p$-Norm Hamming Centroid problem which asks to determine whether some given binary strings have a centroid with a bound on the $p$-norm of its Hamming distances to the strings. Specifically, given a set of strings $S$ and a real $k$, we consider the problem of determining whether there exists a string $s^*$ with $\\big(\\sum_{s \\in S}d^p(s^*,s)\\big)^{1/p} \\leq k$, where $d(,)$ denotes the Hamming distance metric. This problem has important applications in data clustering, and is a generalization of the well-known polynomial-time solvable \\textsc{Consensus String} $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06469","kind":"arxiv","version":3},"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"}