On the approximability of the stable matching problem with ties of size\n two
Bibliographic record
Abstract
The stable matching problem is one of the central problems of algorithmic\ngame theory. If participants are allowed to have ties, the problem of finding a\nstable matching of maximum cardinality is an NP-hard problem, even when the\nties are of size two. Moreover, in this setting it is UGC-hard to provide an\napproximation for the maximum cardinality stable matching problem with a\nconstant factor smaller than 4/3. In this paper, we give a tight analysis of an\napproximation algorithm given by Huang and Kavitha for the maximum cardinality\nstable matching problem with ties of size two, demonstrating an improved\n4/3-approximation factor.\n
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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 | 0.007 | 0.046 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".