Efficient FPT Approaches for Constrained TSP Using Minimum Clique Cover
Bibliographic record
Abstract
In this paper, we present a Fixed-Parameter Tractable (FPT) solution for the well-known Traveling Salesman Problem (TSP). We propose a minimum vertex clique cover algorithm, constrained by a fixed parameter of 2 to 3 vertices. Our approach systematically applies recursive techniques to cover cliques of 2 or 3 vertices, ensuring that the minimal solution to the original decision problem is achieved. The developed technique yields a linear-time FPT solution based on the input number of vertices for a given weighted graph, where each edge e is assigned a non-negative weight w. The graph is composed of multiple subgraphs, and our method identifies the minimum weight subgraphs to efficiently solve the TSP using this vertex-based FPT approach. This framework provides a robust and scalable solution for addressing TSP in weighted graphs.
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How this classification was reachedexpand
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 | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".