Bibliographic record
Abstract
This thesis concerns tree decompositions. Trees are one of the simplest and most well understood class of graphs. A tree decomposition of a graph improves our understanding of the graph in a similar way. For example, as a consequence of Robertson and Seymour's groundbreaking work in the theory of graph minors, there are linear time algorithms for NP-hard problem on graphs that admit a tree decomposition of a certain type. We classify existing tree decompositions and examine what makes a tree decomposition unique. The first result of this thesis is a linear time algorithm for building a tree decomposition for the class of graphs that exclude K 5 as a minor. The second result is a significant modification to this algorithm which results in a linear time algorithm to construct the tree decomposition for graphs which exclude a special set of paths. These are vertex disjoint paths between two pairs of input vertices (s1, t1), (s2, t 2), one from s1 to t 1 and the other from s2 to t 2. We then use these tree decompositions to improve the running time of existing algorithms and extend the allowed input of other algorithms from planar graphs to graphs that exclude K5 as a minor.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.011 | 0.004 |
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".