Some Necessary Conditions and a General Sufficiency Condition for the Validity of A Gilmore-Gomory Type Patching Scheme for the Traveling
Bibliographic record
Abstract
One of the most celebrated polynomially solvable cases of the TSP is the Gilmore-Gomory TSP. The patching scheme for the problem developed by Gilmore and Gomory has several interesting features. Its generalization, called the GG-scheme, has been studied by several researchers and polynomially testable sufficiency conditions for its validity have been given, leading to polynomial schemes for large subclasses of the TSP. A good characterization of the subclass of the TSP for which the GG-scheme produces an optimal solution, is an outstanding open problem of both theoretical and practical significance. We give some necessary conditions and a new, polynomially testable sufficiency condition for the validity of the GG-scheme that properly includes all previously known such conditions. Key words: Traveling salesman problem, Gilmore-Gomory TSP, Patching Scheme, Polynomially solvable cases
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 | 0.031 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.011 | 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".