Bibliographic record
Abstract
ABSTRACT I introduce a new graph‐theoretic property called abundant neighborhoods. This property is motivated by studying the thickness of economic markets. A vertex is, roughly, guaranteed to match if and only if it has an abundant neighborhood. This fact holds across numerous variants of two‐sided markets that are studied across the economics, operations research, and computer science literature. I introduce a new formalism to study these variants under a unifying framework, which I call matching rules, allowing us to study hitherto different types of markets (equivalently, graph matching problems) together. In particular, stable matchings, max‐weight matchings, and rank‐maximal matchings can be studied together as they are all surjective maximal matching rules. Lastly, the abundant neighborhood property can be used to study properties of maximal matchings: a vertex is matched in all maximal matchings if and only if it has an abundant neighborhood. With this observation, I develop a novel decomposition for studying maximal matchings. I use it to introduce a new integer programming formulation of the minimum maximal matching problem, which represents the worst‐case performance of a market. I show with experiments that using this formulation solves the problem for dense graphs with up to 500 vertices with 30%–50% less time than previous approaches from the literature and yields much tighter solutions for timed‐out instances.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".