On the complexity of guarding problems on orthogonal arrangements
Bibliographic record
Abstract
Consider a guard checking on some corridors in a building, the guard does not need to walk the entire length of a corridor, but visits at least one point of a corridor and looks up and down. What is the optimum solution for the guard’s tour? The corridors in a building can be modeled as a system of connected orthogonal arrangement of vertical and horizontal line segments. The optimum problem is transformed into finding the shortest closed path along the line seg-ments touching each line segment at least one point. Since it is a traveling salesman-type problem, we also consider the minimum spanning tree problem in the same model: finding the shortest tree along the line segments touching all line segments. We denote the first problem as a corridor-TSP problem, and denote the second problem as a corridor-MST problem, as shown in Figure 1 below. In this note we claim that these problems are both NP-complete. These two problems belong to minimum length connection problems, which are pre-sented in Canadian Conference of Computational Geometry 2000 [1]. Some corridor problems have been studied in [2] [3].
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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 | 0.020 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.007 | 0.015 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.020 | 0.002 |
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".