Bibliographic record
Abstract
In this thesis we consider constrained geometric optimization problems. The first is a constrained version of the k-Steiner tree problem restricting the Steiner points to lie on a restricted set of curves. We solve the 1-Steiner tree problem in the Euclidean plane in optimal asymptotic time and space bounds when the Steiner point is constrained to lie on an input line. We then show how existing results can be used to generalize the result. The second problem is the smallest k-enclosing disc problem for a point set S contained in a simple polygon. In this problem we work with geodesic discs, meaning we use the geodesic distance function (i.e., the length of the shortest path). We present both a 2-approximation algorithm and an algorithm that finds the optimal radius for the smallest k-enclosing geodesic disc of a set of points inside a simple polygon. The last problem we consider is the smallest k-enclosing geodesic disc problem for a set of points in a simple polygon when the computed disc must be centred on an input chord of the polygon.
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 distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".