Reductions for the stable set problem
Bibliographic record
Abstract
One approach to finding a maximum stable set (MSS) in a graph isto try to reduce the size of the problem by transforming the problem into an equivalent problem on a sma ller graph. This paper introduces several new reductions for the MSS problem, extends several well-known reductionsto the maximum weight stable set (MWSS) problem, demonstrates how reductions for the generalized stable setproblem can be used in conjunction with probing to produce powerful new reductions for both the MSS and MWSS problems, a nd shows how hypergraphs can be used to expand the capabilities of clique projections. The effectivenessof these new reduction techniques are illustrated on the DIM ACS benchmark graphs, planar graphs, and a set of challenging MS S problems arising from Steiner Triple Systems.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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".