{"id":"W1497071043","doi":"10.1007/11496915_5","title":"Disjoint Cycles: Integrality Gap, Hardness, and Approximation","year":2005,"lang":"en","type":"book-chapter","venue":"Lecture notes in computer science","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":17,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo; University of Alberta","funders":"","keywords":"Combinatorics; Disjoint sets; Omega; Packing problems; Mathematics; Approximation algorithm; Vertex (graph theory); Conjecture; Upper and lower bounds; Binary logarithm; Undirected graph; Discrete mathematics; Graph; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002326727,0.001629374,0.002608653,0.002199408,0.00233659,0.006385851,0.004699969,0.003421837,0.009929501],"category_scores_gemma":[0.01733959,0.001581209,0.002095659,0.006539175,0.006032967,0.02023009,0.005482017,0.01082045,0.001008275],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00423217,"about_ca_system_score_gemma":0.001741039,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001441707,"about_ca_topic_score_gemma":0.001127999,"domain_scores_codex":[0.9971517,0.0005049635,0.0001247379,0.0007889705,0.001022111,0.0004075298],"domain_scores_gemma":[0.9859812,0.010808,0.0006526104,0.001585134,0.00045983,0.000513254],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000325315,0.0001781673,0.0009915307,0.0005642265,0.00006028675,0.0001043481,0.000437371,0.01724126,0.0007441933,0.9000229,0.01801097,0.06131934],"study_design_scores_gemma":[0.00002960055,0.00001421369,0.0001558903,0.00005019966,0.00002674819,0.0001149322,0.00007662656,0.01180172,0.0004216395,0.983355,0.003944659,0.000008858721],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1926627,0.02759091,0.5028627,0.03222951,0.001293033,0.0003054752,0.002226964,0.001121808,0.2397069],"genre_scores_gemma":[0.845004,0.01663111,0.09988015,0.00240671,0.003053035,0.0005311226,0.002704232,0.0006337262,0.02915595],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009929501,"threshold_uncertainty_score":0.03321749,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03006902252327674,"score_gpt":0.2571625246057706,"score_spread":0.2270935020824938,"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."}}