Bibliographic record
Abstract
We study a new problem on digraphs, Maximum Directed Linear Arrangement (MaxDLA). This is a directed and maximization variant of the well-studied Minimum Linear Arrangement (MinLA) problem. We relate MaxDLA to the Maximum Directed Cut (MaxDiCut) problem by bounding each in terms of the other. We prove that both MaxDiCut and MaxDLA are NP-Hard for planar digraphs. By contrast, the undirected Maximum Cut problem is known to be polynomial on planar graphs. We present a polynomial algorithm solving MaxDLA on orientations of bounded-degree trees, and, as a by-product, a polynomial algorithm for MinLA on graphs $G$ when $overline{G}$ is a bounded-degree tree. This complements the known fact that MinLA is polynomial-time solvable on trees. Finally, we study maximization analogues of Harper's celebrated isoperimetric inequality for hypercubes. We study tournaments, orientations of graphs with maximum degree at most two, and transitive acyclic digraphs.
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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 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 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".