New Approach to Obtain the Maximum Flow in a Network and Optimal Solution for the Transportation Problems
Bibliographic record
Abstract
The maximum flow problem is also one of the highly regarded problems in the field of optimization theory in which the objective is to find a feasible flow through a flow network that obtains the maximum possible flow rate from source to sink. The literature demonstrates that different techniques have been developed in the past to handle the maximum amount of flow that the network can handle. The Ford-Fulkerson algorithm and Dinic's Algorithm are the two major algorithms for solving these types of problems. Also, the Max-Flow Min-Cut Theorem, the Scaling Algorithm, and the Push–relabel maximum flow algorithm are the most acceptable methods for finding the maximum flows in a flow network. In this novel approach, the paper develops an alternative method of finding the maximum flow between the source and target nodes of a network based on the "max-flow." Also, a new algorithmic approach to solving the transportation problem (minimizing the transportation cost) is based upon the new maximum flow algorithm. It is also to be noticed that this method requires a minimum number of iterations to achieve optimality. This study's algorithmic approach is less complicated than the well-known meta-heuristic algorithms in the literature.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".