{"id":"W4416902920","doi":"10.1137/24m1635570","title":"Exact Algorithms and Lower Bounds for Stable Instances of Euclidean \\(\\boldsymbol{k}\\)- <scp>means</scp>","year":2025,"lang":"en","type":"article","venue":"SIAM Journal on Computing","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina; University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Euclidean geometry; Approximation algorithm; Upper and lower bounds; Time complexity; Euclidean domain; Euclidean distance","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00514006,0.00411941,0.003480199,0.003423261,0.003594494,0.0108627,0.01153312,0.005091299,0.03828036],"category_scores_gemma":[0.03737422,0.002038192,0.003692809,0.007146679,0.004213593,0.01662463,0.007509323,0.009172278,0.006556437],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.007616015,"about_ca_system_score_gemma":0.007833195,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.005680264,"about_ca_topic_score_gemma":0.0150474,"domain_scores_codex":[0.9931167,0.001530926,0.0003402503,0.001866427,0.001576849,0.001568842],"domain_scores_gemma":[0.965248,0.02356062,0.002208001,0.005030678,0.002205673,0.001746962],"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":[0.002696066,0.001534787,0.003728815,0.001642763,0.0003874399,0.0002292911,0.0006624875,0.3244841,0.004455024,0.4223743,0.09880476,0.1390003],"study_design_scores_gemma":[0.0001825773,0.0001312182,0.0006048867,0.0001081732,0.00010768,0.0001440126,0.0001822014,0.5907785,0.002194232,0.4020477,0.003466079,0.00005265412],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1616374,0.005721701,0.7044347,0.01396305,0.001474941,0.0007839609,0.007108552,0.005515757,0.09935988],"genre_scores_gemma":[0.6063517,0.001815641,0.3498165,0.002142584,0.001255666,0.0008134715,0.009270215,0.003520181,0.02501394],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03828036,"threshold_uncertainty_score":0.1280606,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01877987908988277,"score_gpt":0.2781844359888292,"score_spread":0.2594045568989464,"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."}}