{"id":"W2042788891","doi":"10.1016/j.orl.2010.09.004","title":"Integrality gap of the hypergraphic relaxation of Steiner trees: A short proof of a 1.55 upper bound","year":2010,"lang":"en","type":"article","venue":"Operations Research Letters","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Steiner tree problem; Linear programming relaxation; Hypergraph; Mathematics; Upper and lower bounds; Combinatorics; Bounded function; Relaxation (psychology); Linear programming; Tree (set theory); Approximation algorithm; Discrete mathematics; Algorithm; Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.001511372,0.00009244034,0.0001724965,0.0003497125,0.0002598796,0.00007856858,0.001213485,0.0000591387,0.00003728],"category_scores_gemma":[0.0004000071,0.00006369701,0.0001409803,0.001543374,0.0009123703,0.0003916521,0.000315493,0.0005479521,0.000001666854],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000196386,"about_ca_system_score_gemma":0.0001856435,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007776275,"about_ca_topic_score_gemma":0.00195786,"domain_scores_codex":[0.9979404,0.0003603797,0.0003955873,0.0002571813,0.0008181876,0.0002282186],"domain_scores_gemma":[0.9980973,0.0001761611,0.00005038692,0.001043564,0.0005828796,0.00004972643],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.00001709073,0.0004443048,0.009196136,0.00007073665,0.00006632475,0.000001371019,0.002399621,0.002095982,0.7614553,0.2113337,0.001727064,0.01119237],"study_design_scores_gemma":[0.001072936,0.0004821678,0.117923,0.0003395072,0.00003267389,0.00002842737,0.0005639892,0.3653974,0.4963423,0.01357961,0.00369542,0.0005425209],"study_design_candidate":"bench_or_experimental","study_design_consensus":"bench_or_experimental","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9697189,0.0000236902,0.02102113,0.008056075,0.0001821272,0.0004430868,0.00001554474,0.0000121698,0.0005272772],"genre_scores_gemma":[0.9880609,0.000005468752,0.01164521,0.0000880904,0.00003246388,0.00004649854,0.000003819035,0.000005961148,0.000111569],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3633014,"threshold_uncertainty_score":0.3361667,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06305174887661538,"score_gpt":0.3385172516865786,"score_spread":0.2754655028099633,"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."}}