Some Complexity Results for Metric View Planning Problem With Traveling Cost and Visibility Range
Bibliographic record
Abstract
In this paper, we consider the problem where a point robot in a 2D or 3D environment equipped with an omnidirectional range sensor of finite range D is asked to cover a set of surface patches, while minimizing the sum of view cost, proportional to the number of viewpoints planned, and the travel cost, proportional to the length of path traveled. We call it the Metric View Planning Problem with Traveling Cost and Visibility Range or Metric TVPP in short. We present a complexity result for the problem, i.e., we show that the Metric TVPP cannot be approximated within O(log m) ratio by any polynomial algorithm, where m is the number of surface patches to cover. We then analyze a variant of an existing decoupled two-level algorithm of first solving the view planning problem to get an approximate solution, and then solving, again using an approximation algorithm, the Metric traveling salesman problem to connect the planned viewpoints. We then present performance bounds for this two-level decoupled algorithm, i.e., we show that it has an approximation ratio of O(log m). Thus, it asymptotically achieves the best approximation ratio one can hope for.
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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 | 0.013 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.010 | 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".