{"paper":{"title":"Various complexity results for computational mass spectrometry problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Francois Nicolas, Sebastian B\\\"ocker","submitted_at":"2011-09-15T14:42:48Z","abstract_excerpt":"Define Minimum Soapy Union (MinSU) as the following optimization problem: given a $k$-tuple $(X_1, X_2,..., X_k)$ of finite integer sets, find a $k$-tuple $(t_1, t_2,..., t_k)$ of integers that minimizes the cardinality of $(X_1 + t_1) \\cup (X_2 + t_2) \\cup ... \\cup (X_n + t_k)$. We show that MinSU is NP-complete, APX-hard, and polynomial for fixed $k$. MinSU appears naturally in the context of protein shotgun sequencing: Here, the protein is cleaved into short and overlapping peptides, which are then analyzed by tandem mass spectrometry. To improve the quality of such spectra, one then asks f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3367","kind":"arxiv","version":4},"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"}