{"paper":{"title":"UPGMA and the normalized equidistant minimum evolution problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"q-bio.PE","authors_text":"Andreas Spillner, Taoyang Wu, Vincent Moulton","submitted_at":"2017-04-03T09:38:33Z","abstract_excerpt":"UPGMA (Unweighted Pair Group Method with Arithmetic Mean) is a widely used clustering method. Here we show that UPGMA is a greedy heuristic for the normalized equidistant minimum evolution (NEME) problem, that is, finding a rooted tree that minimizes the minimum evolution score relative to the dissimilarity matrix among all rooted trees with the same leaf-set in which all leaves have the same distance to the root. We prove that the NEME problem is NP-hard. In addition, we present some heuristic and approximation algorithms for solving the NEME problem, including a polynomial time algorithm tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00497","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"}