Bibliographic record
Abstract
We introduce and study various patrolling algorithms using mobile robots.A team of k mobile robots (patrolmen), is deployed on a weighted graph G, in which edge weights represent distances.The robots perpetually move along the domain not exceeding their maximal speed.The robots need to patrol the graph by regularly visiting all points of the domain.The goal of the patrolling problem is to find the perpetual movement of the robots minimizing idle time, which is the maximal time when a point of the graph remains unseen by any robot.In this thesis, we investigate various versions of patrolling problems, in each case attempting to optimize the idle time.In the first scenario, we consider a case where at most f of k robots may be faulty (unreliable), i.e., they do not report their monitoring activities.We design an optimal algorithm for the open curves (segments), and then use these results to study the case of general graphs.We also propose an optimal patrolling strategy for Eulerian graphs.Afterward, we show that computing idle time for three robots, at most one of which is faulty, is NP-hard for some general graphs.Next, we study the patrolling problem by reliable robots, but equipped with distinct visibility ranges, i.e., every robot i has a range of visibility r i representing the distance from its current position, at which the robot can see in each direction.We give the optimal patrolling algorithms for the case of close curves (cycles) and open curves (segments), when all robots have the same maximal speed and different visibility ranges.We also briefly discuss the case where robots have distinct speeds and visibility ranges to show that patrolling by robots equipped with visibility is entirely different than the case of robots with zero visibility.Moreover, we show that patrolling general graphs by robots with the same speed and distinct visibility ranges is NP-hard.Finally, we consider patrolling trees by a team of mobile robots with the same speed and zero visibility.We theoretically show the optimality of an off-line centralized algorithm for trees patrolling.Then, we use these results to experimentally show the efficiency of an on-line distributed algorithm (known as rotor-router) for trees patrolling.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".