{"id":"W4414646315","doi":"10.1007/978-3-032-06706-7_14","title":"Online Algorithm for Fractional Matchings with Edge Arrivals in Graphs of Maximum Degree Three","year":2025,"lang":"en","type":"book-chapter","venue":"Lecture notes in computer science","topic":"Optimization and Search Problems","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto; University of Waterloo","funders":"","keywords":"Competitive analysis; Bipartite graph; Vertex (graph theory); Hopcroft–Karp algorithm; Degree (music); Cardinality (data modeling); Online algorithm; Graph","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"],"consensus_categories":[],"category_scores_codex":[0.0007374282,0.0003827794,0.0005433644,0.00136139,0.0001386862,0.0002040022,0.002285686,0.0002359482,0.00001460371],"category_scores_gemma":[0.00006110246,0.0003239632,0.0001169146,0.000965932,0.0004771288,0.0005271534,0.0006583625,0.0006464562,0.000002091324],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001498275,"about_ca_system_score_gemma":0.0009240592,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005561906,"about_ca_topic_score_gemma":0.0005349558,"domain_scores_codex":[0.9969375,0.00002497822,0.0005725027,0.00109721,0.0008645739,0.0005032799],"domain_scores_gemma":[0.9976808,0.0006431419,0.0003001427,0.0007839184,0.0004809791,0.0001109819],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00001114887,0.00009763159,0.0001678918,0.00007716627,0.00001642574,0.00001625346,0.000234176,0.04381395,0.00001306453,0.0274992,0.00003084207,0.9280223],"study_design_scores_gemma":[0.0004927721,0.0001889074,0.0002579553,0.0004841256,0.000004160878,0.00001261546,1.973627e-7,0.7099964,0.0001080691,0.2876555,0.0005082858,0.0002910022],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0000251733,0.0001365037,0.9964434,0.001060762,0.0005822201,0.0007492302,0.0000403986,0.00006549543,0.0008968439],"genre_scores_gemma":[0.001791309,0.00003722365,0.9969296,0.0008196051,0.0000906663,0.00002235637,0.00001991493,0.00001976407,0.0002695644],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.9277313,"threshold_uncertainty_score":0.9999213,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02830691949131343,"score_gpt":0.2735100315596817,"score_spread":0.2452031120683683,"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."}}