{"id":"W2057259762","doi":"10.1007/s00454-001-0042-y","title":"Every Set of Disjoint Line Segments Admits a Binary Tree","year":2001,"lang":"en","type":"article","venue":"Discrete & Computational Geometry","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":28,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University; Carleton University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Mathematics; K-ary tree; Disjoint sets; Tree (set theory); Interval tree; Binary tree; Vertex (graph theory); Segment tree; Line segment; Range tree; Line (geometry); Plane (geometry); Discrete mathematics; Tree structure; Graph; Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0004124945,0.0002802059,0.0003391327,0.0007331921,0.0001846225,0.0001093655,0.0006856067,0.00009326768,0.0001127891],"category_scores_gemma":[0.0001128206,0.0002781015,0.0002027499,0.002369869,0.00008196704,0.0007796745,0.0003757518,0.0001764347,0.00009806072],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007618452,"about_ca_system_score_gemma":0.0002170348,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000164733,"about_ca_topic_score_gemma":0.00000412731,"domain_scores_codex":[0.997271,0.0001216492,0.0006712968,0.0006028103,0.0009693928,0.0003638348],"domain_scores_gemma":[0.998332,0.0003543244,0.0003034544,0.0004117756,0.0003979751,0.0002005059],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001325579,0.0004227756,0.00775465,0.00008718013,0.0002135367,0.00009086523,0.0005614457,0.844601,0.001665445,0.03998468,0.002665265,0.1018206],"study_design_scores_gemma":[0.001462613,0.0005350253,0.1554805,0.000093225,0.00003246415,0.0001412827,0.00007122123,0.8102365,0.001085369,0.02614873,0.004106784,0.0006063641],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3400151,0.0003420688,0.6568164,0.000901814,0.0004237189,0.0002022328,0.00004401125,0.0001139461,0.001140695],"genre_scores_gemma":[0.9439524,0.00003175814,0.05417444,0.0004308507,0.0002455733,0.00001981275,0.0004698477,0.00001761715,0.0006576272],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6039373,"threshold_uncertainty_score":0.9999671,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02535542343954046,"score_gpt":0.2833968965844862,"score_spread":0.2580414731449457,"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."}}