Bibliographic record
Abstract
List partitions generalize list colourings and list homomorphisms. Each symmetric matrix M over 0; 1; defines a list partition problem. Different choices of the matrix M lead to many well-known graph theoretic problems including the problem of recognizing split graphs and their generalizations, finding homogeneous sets, joins, clique cutsets, stable cutsets, skew cutsets and so on. We develop tools which allow us to classify the complexity of many list partition problems and, in particular, yield the complete classification for small matrices M . Along the way, we obtain a variety of specific results including: generalizations of Lov'asz's communication bound on the number of cliqueversus -stable-set separators; polynomial-time algorithms to recognize generalized split graphs; a polynomial algorithm for the list version of the Clique Cutset Problem; and the first subexponential algorithm for the Skew Cutset Problem of Chv'atal. We also show that the dichotomy (NP -complete versus polynomial-time solvable), conjectured for certain graph homomorphism problems would, if true, imply a slightly weaker dichotomy (NP -complete versus quasipolynomial) for our list partition problems 1 . E-mail: tomas@theory.stanford.edu. y School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada, V5A1S6. E-mail: pavol@cs.sfu.ca. Supported by a Research Grant from the National Sciences and Engineering Research Council. z Departamento da Ciencia da Computac~ao - I.M., COPPE/Sistemas, Universidade Federal do Rio de Janeiro, RJ, 21945-970, Brasil. E-mail: sula@cos.ufrj.br. Supported by CNPq and PRONEX 107/97. x Department of Computer Science, Stanford University, CA 94305-9045. E-mail: rajeev@cs.stanford.edu. Supported by an ARO MURI Grant DAAH04--96--1...
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.004 | 0.001 |
| Scholarly communication | 0.008 | 0.012 |
| Open science | 0.004 | 0.007 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.276 | 0.159 |
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".