Faster Algorithms for Semi-Matching Problems
Bibliographic record
Abstract
We consider the problem of finding semi-matching in bipartite graphs, which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted cases. For the weighted case, we give an O ( nm log n )-time algorithm, where n is the number of vertices and m is the number of edges, by exploiting the geometric structure of the problem. This improves the classical O ( n 3 )-time algorithms by Horn [1973] and Bruno et al. [1974b]. For the unweighted case, the bound can be improved even further. We give a simple divide-and-conquer algorithm that runs in O (√ nm log n ) time, improving two previous O ( nm )-time algorithms by Abraham [2003] and Harvey et al. [2003, 2006]. We also extend this algorithm to solve the Balanced Edge Cover problem in O (√ nm log n ) time, improving the previous O ( nm )-time algorithm by Harada et al. [2008].
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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 | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.011 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.021 | 0.006 |
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".