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 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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".