Solving Graph Coloring Problems Using Cultural Algorithms.
Bibliographic record
Abstract
In this paper, we combine a novel Sequential Graph Coloring Heuristic Algorithm (SGCHA) with a non-systematic method based on a cultural algorithm to solve the graph coloring problem (GCP). The GCP involves finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. In our solving approach, we first use an estimator which is implemented with SGCHA to predict the minimum colors. Then, in the non-systematic part which has been designed using cultural algorithms, we improve the prediction. Various components of the cultural algorithm have been implemented to solve the GCP with a self adaptive behavior in an efficient manner. As a result of utilizing the SGCHA and a cultural algorithm, the proposed method is capable of finding the solution in a very efficient running time. The experimental results show that the proposed algorithm has a high performance in time and quality of the solution returned for solving graph coloring instances taken from DIMACS website. The quality of the solution is measured here by comparing the returned solution with the optimal one.
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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 | 0.006 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".