A near-linear time approximation scheme for geometric transportation with arbitrary supplies and spread
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.
Bibliographic record
Abstract
$\newcommand{\R}{\mathbb{R}}\DeclareMathOperator{\poly}{poly}\DeclareMathOperator{\polylog}{polylog}$The geometric transportation problem takes as input a set of points \(P\) in \(d\)-dimensional Euclidean space and a supply function \(\mu : P \to \R\). The goal is to find a transportation map, a non-negative assignment \(\tau : P \times P \to \R_{\geq 0}\) to pairs of points, so the total assignment leaving each point is equal to its supply, i.e., \(\sum_{r \in P} \tau(q, r) - \sum_{p \in P} \tau(p, q) = \mu(q)\) for all points \(q \in P\). The goal is to minimize the weighted sum of Euclidean distances for the pairs, \(\sum_{(p, q) \in P \times P} \tau(p, q) \cdot ||q - p||_2\). We describe the first algorithm for this problem that returns, with high probability, a \((1 + \epsilon)\)-approximation to the optimal transportation map in \(O(n \poly(1 / \epsilon) \polylog{n})\) time. In contrast to the previous best algorithms for this problem, our near-linear running time bound is independent of the spread of \(P\) and the magnitude of its real-valued supplies.
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 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 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 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 it