{"paper":{"title":"Lower Bounds for Optimal Alignments of Binary Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"q-bio.GN","authors_text":"Cynthia Vinzant","submitted_at":"2008-07-01T01:29:06Z","abstract_excerpt":"In parametric sequence alignment, optimal alignments of two sequences are computed as a function of the penalties for mismatches and spaces, producing many different optimal alignments. Here we give a 3/(2^{7/3}\\pi^{2/3})n^{2/3} +O(n^{1/3} \\log n) lower bound on the maximum number of distinct optimal alignment summaries of length-n binary sequences. This shows that the upper bound given by Gusfield et. al. is tight over all alphabets, thereby disproving the \"square root of n conjecture\". Thus the maximum number of distinct optimal alignment summaries (i.e. vertices of the alignment polytope) o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0051","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"}