Calculating the meeting point of scattered robots on weighted terrain surfaces
Bibliographic record
Abstract
In this paper we discuss the problem of determining a meeting point of a set of scattered robots R = {r1,r2,...,rs} in a weighted terrain P which has n> s triangular faces. Our algorithmic approach is to produce a discretization of P by producing a graph G = {V G,E G} which lies on the surface of P. For a chosen vertex p ′ ∈ V G, we define ‖Π(ri,p ′)‖ as the minimum weight cost of traveling from ri to p ′. We show that minp ′ ∈V G{max1≤i≤s{‖Π(ri,p ′)‖}} ≤ minp∗∈P{max1≤i≤s{‖Π(ri,p ∗)‖}} + W |L | where L is the longest edge of P, W is the maximum cost weight of a face of P, and p ∗ is the optimal solution. Our algorithm requires O(snmlog(snm)+snm 2) time to run, where m = n in the Euclidean metric and m = n2 in the weighted metric. However, we show through experimentation that only a constant value of m is required (e.g., m=8) in order to produce very accurate solutions (< 1 % error). Hence, for typical terrain data, the expected running time of our algorithm is O(snlog(sn)). Also, as part of our experiments we show that by using geometrical subsets (i.e., 2D/3D convex hulls, 2D/3D bounding boxes and random selection) of the robots we can improve the running time for finding p ′, with minimal or no additional accuracy error when comparing p ′ to p ∗. 1
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".