The multiroute maximum flow problem revisited
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We are given a directed network G = ( V , A , u ) with vertex set V , arc set A , a source vertex s ∈ V , a destination vertex t ∈ V , a finite capacity vector u = { u ij } ( i , j )∈ A , and a positive integer m ∈ Z + . The multiroute maximum flow problem ( m ‐MFP) generalizes the ordinary maximum flow problem by seeking a maximum flow from s to t subject to not only the regular flow conservation constraints at the vertices (except s and t ) and the flow capacity constraints at the arcs, but also the extra constraints that any flow must be routed along m arc‐disjoint s ‐ t paths. In this article, we devise two new combinatorial algorithms for m ‐MFP. One is based on Newton's method and another is based on an augmenting‐path technique. We also show how the Newton‐based algorithm unifies two existing algorithms, and how the augmenting‐path algorithm is strongly polynomial for case m = 2. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(2), 81–92 2006
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it