A More Accurate Metaheuristic Approach for the Art Gallery Problem
Bibliographic record
Abstract
The Art Gallery problem is one of the most important non-deterministic polynomial (NP)-hard optimization problems in computational geometry, with many applications in localization, robotics, telecommunications, etc. The goal of the Art Gallery problem is to find the minimum number of guards needed within a simple polygon to observe and protect its entirety. There are several approaches to solving the Art Gallery problem, and this paper presents an efficient method based on the Particle Filter algorithm, which solves the most fundamental case of the problem in a nearly optimal manner. Experimental results on random polygons generated show that the new method is more accurate, providing solutions that are, on average, 9.94% better than Bottino's results for the same sample set. The approach was also applied to four groups of random orthogonal polygons and compared with the optimal solution. Results show that the new method finds the optimal solution with a 0.16% error. Furthermore, this paper discusses the impact of resampling and particle numbers in minimizing runtime.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".