Bibliographic record
Abstract
By the DAG decomposition, we mean the decomposition of a directed acyclic graph G into a minimized set of node-disjoint chains, which cover all the nodes of G. For any two nodes u and v on a chain, if u is above v then there is a path from u to v in G. In this paper, we discuss an efficient algorithm for this problem. Its time complexity is bounded by O(max{k, } ×n2) while the best algorithm for this problem up to now needs O(n3) time, where n is the number of the nodes of G, and k is G’s width, defined to be the size of a largest node subset U of G such that for every pair of nodes x, y Î U, there does not exist a path from x to y or from y to x. k is in general much smaller than n. In addition, by the existing algorithm, Q(n2) extra space (besides the space for G itself) is required to maintain the transitive closure of G to do the task while ours needs only O(k×n) extra space. This is particularly important for some nowadays applications with massive graphs including millions and even billions of nodes, like the facebook, twitter, and some other social networks.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.015 | 0.004 |
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".