Worst-Case Solution Quality Analysis When Not Re-Expanding Nodes in Best-First Search
Bibliographic record
Abstract
The use of inconsistent heuristics with A* can result in increased runtime due to the need to re-expand nodes. Poor performance can also be seen with Weighted A* if nodes are re-expanded. While the negative impact of re-expansions can often be minimized by setting these algorithms to never expand nodes more than once, the result can be a lower solution quality. In this paper, we formally show that the loss in solution quality can be bounded based on the amount of inconsistency along optimal solution paths. This bound holds regardless of whether the heuristic is admissible or inadmissible, though if the heuristic is admissible the bound can be used to show that not re-expanding nodes can have at most a quadratic impact on the quality of solutions found when using A*. We then show that the bound is tight by describing a process for the construction of graphs for which a best-first search that does not re-expand nodes will find solutions whose quality is arbitrarily close to that given by the bound. Finally, we will use the bound to extend a known result regarding the solution quality of WA* when weighting a consistent heuristic, so that it also applies to other types of heuristic weighting.
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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 | 0.010 | 0.050 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".