Minimum ratio canceling is oracle polynomial for linear programming, but not strongly polynomial, even for networks
Bibliographic record
Abstract
This paper shows that the minimum ratio canceling algorithm (and a faster relaxed version) of Wallacher (1989) can be generalized to an algorithm for general linear programs with geometric convergence. This implies that when we have a negative cycle oracle, this algorithm will compute an optimal solution in (weakly) polynomial time. We then specialize the algorithm to linear programming on unimodular linear spaces, and to the minimum cost ow and (dual) tension problems. We construct instances proving that even in the network special cases the algorithm is not strongly polynomial. Keywords: negative cycle canceling algorithm, minimum ratio cycle, linear programming problem, unimodular linear space, minimum cost ow, minimum cost tension. 1 Introduction A popular class of algorithms for the minimum cost ow problem is the cycle canceling algorithms. This concept originates with Klein [11], and is based on the idea that pushing ow around negative-cost residual cycles will impr...
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.008 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 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".