Depth-first discovery algorithm for incremental topological sorting of directed acyclic graphs
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
We study the problem of incrementally maintaining a topological sorting in a large DAG. The Discovery Algorithm (DA) of Alpern et al. [Proc. 1st Annual ACM-SIAM Symp. on Discrete Algorithms, 1990, pp. 32-42] computes a cover K of nodes such that a solution to the modified problem can be found by changing node priorities within K only. It achieves a runtime complexity that is polynomially bounded in terms of the minimal cover size k.The temporary space complexity of DA grows quickly with increasing number of added edges and cover size. We introduce the Depth-First Discovery Algorithm (DFDA), which uses depth-first search to reduce the temporary space of DA from O(|A| × ||-K||) to O(|A| + ||K||), where |A| is the number of edges to add and ||K|| is the extended size of the cover. DFDA is simpler than DA and performs better in our empirical tests.
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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it