Voronoi games and epsilon nets
Bibliographic record
Abstract
Competitive facility location is concerned with the strategic placement of facilities by competing market players. In the Discrete Voronoi Game V G(k, l), two players P1 and P2, respectively, strive to attract as many of n users as possible. Initially, P1 first chooses a set F of k locations in the plane to place its facilities. Then, P2 chooses a set S of l locations in the plane to place its facilities, where S ∩ F = ∅. Finally, the users choose the facilities based on the nearest-neighbour rule. The goal for each player is to maximize the number of users served by its set of facilities. By establishing a connection between V G(2, 1) and -nets, we provide an algorithm running in O(n log4 n) time to find a 74-factor approximation of the optimal strategy of P1 in V G(2, 1). We also prove that for any real number 0 < α < 1, there exists a placement of 42α facilities by P1 such that P2 can serve at most αn users by placing one facility. 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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.000 |
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.
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".