{"paper":{"title":"Minimum Segmentation for Pan-genomic Founder Reconstruction in Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Bastien Cazaux, Dmitry Kosolobov, Tuukka Norri, Veli M\\\"akinen","submitted_at":"2018-05-09T15:04:25Z","abstract_excerpt":"Given a threshold $L$ and a set $\\mathcal{R} = \\{R_1, \\ldots, R_m\\}$ of $m$ haplotype sequences, each having length $n$, the minimum segmentation problem for founder reconstruction is to partition the sequences into disjoint segments $\\mathcal{R}[i_1{+}1,i_2], \\mathcal{R}[i_2{+}1, i_3], \\ldots, \\mathcal{R}[i_{r-1}{+}1, i_r]$, where $0 = i_1 < \\cdots < i_r = n$ and $\\mathcal{R}[i_{j-1}{+}1, i_j]$ is the set $\\{R_1[i_{j-1}{+}1, i_j], \\ldots, R_m[i_{j-1}{+}1, i_j]\\}$, such that the length of each segment, $i_j - i_{j-1}$, is at least $L$ and $K = \\max_j\\{ |\\mathcal{R}[i_{j-1}{+}1, i_j]| \\}$ is mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03574","kind":"arxiv","version":2},"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"}