{"paper":{"title":"O-notation in algorithm analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kalle Rutanen","submitted_at":"2013-09-12T16:21:46Z","abstract_excerpt":"We provide an extensive list of desirable properties for an O-notation --- as used in algorithm analysis --- and reduce them to 8 primitive properties. We prove that the primitive properties are equivalent to the definition of the O-notation as linear dominance. We abstract the existing definitions of the O-notation under local linear dominance, and show that it has a characterization by limits over filters for positive functions. We define the O-mappings as a general tool for manipulating the O-notation, and show that Master theorems hold under linear dominance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3210","kind":"arxiv","version":32},"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"}