Bibliographic record
Abstract
We examine formulations for the well-known b-matching problem in the presence of integer demands on the edges. A subset M of edges is feasible if for each node v the total demand of edges in M incident to v is at most bv. We examine the system of star inequalities for this problem. This system yields an exact linear description for b-matchings in bipartite graphs. For the demand version, we show that the integrality gap for this system is at least 2.5 and at most 2.764. For general graphs, the gap lies between 3 and 3.264. We also describe a 3-approximation algorithm (2.5 for bipartite graphs) for the cardinality version of the problem. A fully polynomial approximation scheme is also presented for the problem on a tree, thus generalising a well-known result for the knapsack problem. Recently, the notion of demand matching has arisen in the design of Clos network switches.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.004 | 0.002 |
| Insufficient payload (model declined to judge) | 0.026 | 0.003 |
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".