Modeling the Parallelization of the Edmonds-Karp Algorithm and Application
Bibliographic record
Abstract
Many optimization problems can be reduced to the maximum flow problem in a network. However, the maximum flow problem is equivalent to the problem of the minimum cut, as shown by Fulkerson and Ford (Fulkerson & Ford, 1956). There are several algorithms of the graph’s cut, such as the Ford-Fulkerson algorithm (Ford & Fulkerson, 1962), the Edmonds-Karp algorithm (Edmonds & Karp, 1972) or the Goldberg-Tarjan algorithm (Goldberg & Tarjan, 1988). In this paper, we study the parallel computation of the Edmonds-Karp algorithm which is an optimized version of the Ford-Fulkerson algorithm. Indeed, this algorithm, when executed on large graphs, can be extremely slow, with a complexity of the order of O|V|.|E|2 (where |V| designates the number of vertices and |E| designates the number of the edges of the graph). So why we are studying its implementation on inexpensive parallel platforms such as OpenMp and GP-GPU. Our work also highlights the limits for parallel computing on this algorithm.
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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".