{"id":"W4402816864","doi":"10.2139/ssrn.4957990","title":"Tight Upper and Lower Bounds for the Quadratic Knapsack Problem Through Binary Decision Diagrams","year":2024,"lang":"en","type":"preprint","venue":"SSRN Electronic Journal","topic":"Optimization and Packing Problems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Knapsack problem; Binary number; Quadratic equation; Mathematics; Binary decision diagram; Combinatorics; Upper and lower bounds; Mathematical optimization; Algorithm; Arithmetic; Mathematical analysis; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","research_integrity"],"consensus_categories":[],"category_scores_codex":[0.00111455,0.0003911688,0.0003252921,0.0001172424,0.0002900414,0.0006106957,0.0003705407,0.0003153575,0.00005136527],"category_scores_gemma":[0.00003191566,0.0002647618,0.0002472585,0.0001722045,0.00006127631,0.0001216068,0.0002791281,0.003831076,0.00003458986],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005527696,"about_ca_system_score_gemma":0.0007830678,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001172232,"about_ca_topic_score_gemma":0.0001932236,"domain_scores_codex":[0.9974521,0.00003930031,0.0004782699,0.0003323314,0.0002676043,0.001430363],"domain_scores_gemma":[0.9991889,0.000226413,0.0001020389,0.0003233845,0.00008779742,0.00007146211],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001530042,0.0001194631,0.0001321982,0.001283723,0.002429881,0.00001419734,0.003004072,0.6903448,0.0001050704,0.1544066,0.01940088,0.1286061],"study_design_scores_gemma":[0.0004551599,0.0002144383,0.00001614316,0.0005603236,0.0002417707,0.000227876,0.0001914144,0.1221964,0.00001692874,0.8458629,0.02957666,0.0004399534],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01998368,0.1962522,0.7648765,0.004110194,0.007483561,0.002223294,0.00004553099,0.0006110199,0.004414085],"genre_scores_gemma":[0.87243,0.1119035,0.009144193,0.0001800463,0.001298219,0.0002263088,0.00005664595,0.0003226859,0.004438462],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8524463,"threshold_uncertainty_score":0.9999804,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009506888782251517,"score_gpt":0.2455014864579759,"score_spread":0.2359945976757244,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}