Farthest Neighbor Voronoi Diagram in the Presence of Rectangular Obstacles.
Bibliographic record
Abstract
We propose an implicit representation for the farthest Voronoi diagram of a set P of n points in the plane located outside a set R of m disjoint axes-parallel rec-tangular obstacles. The distances are measured ac-cording to the L1 shortest path (geodesic) metric. In particular, we design a data structure of size O(N1.5) in O(N1.5 log2N) time that supports O(N0.5 logN)-time farthest point queries (where N = m + n). We avoid computing the more complicated farthest neigh-bor Voronoi diagram, whose combinatorial complexity is Θ(mn). This allows one to compute the diameter (and all farthest pairs) of P in O(N1.5 log2N) time. This improves the previous O(mn logN) bound [1]. 1
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".