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Record W1562525740 · doi:10.1002/rsa.10099

One line and n points

2003· article· en· W1562525740 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueRandom Structures and Algorithms · 2003
Typearticle
Languageen
FieldComputer Science
TopicComputational Geometry and Mesh Generation
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsComputer scienceLine (geometry)MathematicsGeometry

Abstract

fetched live from OpenAlex

Abstract We analyze a randomized pivoting process involving one line and n points in the plane. The process models the behavior of the R ANDOM ‐E DGE simplex algorithm on simple polytopes with n facets in dimension n − 2. We obtain a tight O (log 2 n ) bound for the expected number of pivot steps. This is the first nontrivial bound for R ANDOM ‐E DGE , which goes beyond bounds for specific polytopes. The process itself can be interpreted as a simple algorithm for certain 2‐variable linear programming problems, and we prove a tight Θ( n ) bound for its expected runtime. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.767
Threshold uncertainty score0.285

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.013
GPT teacher head0.239
Teacher spread0.226 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it