Bibliographic record
Abstract
Given n lines in the plane, a (1/r)-cutting is a subdivision of the plane into cells such that each cell intersects at most n/r lines. Cuttings are fundamental to the design of geometric divide-and-conquer algorithms and have numerous applications. Early suboptimal constructions of cuttings were given implicitly in the works by Megiddo and by Dyer in the 80s; simple randomized constructions were later discovered by Clarkson and by Haussler and Welzl; subsequently deterministic algorithms were given by Chazelle and Friedman, by Matousek, and by Agarwal; eventually O(nr)-time deterministic algorithms to construct (1/r)-cuttings of optimal O(r) size were obtained by Matousek and by Chazelle in the early 90s. In this talk, I will survey some of these past works. I will also give a self-contained presentation of an O(nr)-time deterministic algorithm in 2D which does not require any background on derandomization techniques and which (I hope) is easy to understand.
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.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.015 | 0.005 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".