The least-used direction pivot rule on acyclic unique sink orientations
Bibliographic record
Abstract
The least-used direction (LUD) rule is one of a class of largely unanalyzed pivot rules - the history-based rules. History-based pivot rules guide the progression of edge following algorithms like the Simplex method. This thesis investigates the problem of finding an exponential length LUD path on a particular kind of digraph known as an acyclic unique sink orientation of a hypercube (AUSO). In addition, a survey of six well-known history-based pivot rule and examples to illustrate their independence is given. The Fibonacci construction is introduced as a potential way of creating families of AUSOs that allows for exponential LUD paths. The most straight-forward application of this technique is unsuccessful, but there is room for more exploration. An exponential lower bound is given for thenumber of times the least-used direction is used by a Hamiltonian path following the related history-based Zadeh's rule. This result shows that the number of times each direction is used grows at a similar rate and is thus relatively balanced.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".