Relaxed Most Negative Cycle and Most Positive Cut Canceling Algorithms for Minimum Cost Flow
Bibliographic record
Abstract
This paper presents two new scaling algorithms for the minimum cost network flow problem, one a primal cycle canceling algorithm, the other a dual cut canceling algorithm. Both algorithms scale a relaxed optimality parameter, and create a second, inner relaxation. The primal algorithm uses the inner relaxation to cancel a most negative node-disjoint family of cycles w.r.t. the scaled parameter, the dual algorithm uses it to cancel most positive cuts w.r.t. the scaled parameter. We show that in a network with n nodes and m arcs, both algorithms need to cancel only O(mn) objects per scaling phase. Furthermore, we show how to efficiently implement both algorithms to yield weakly polynomial running times that are as fast as any other cycle or cut canceling algorithms. Our algorithms have potential practical advantages compared to some other canceling algorithms as well. Along the way, we give a comprehensive survey of cycle and cut canceling algorithms for min-cost flow. We also clarify the formal duality between cycles and cuts.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".