Min-Max Vertex Cycle Covers With Connectivity Constraints for Multi-Robot Patrolling
Bibliographic record
Abstract
We consider a multi-robot patrolling scenario with intermittent connectivity constraints, ensuring that robots' data finally arrive at a base station. In particular, each robot traverses a closed tour periodically and meets with the robots on neighboring tours to exchange data. We model the problem as a variant of the min-max vertex cycle cover problem (MMCCP), which is the problem of covering all vertices with a given number of disjoint tours such that the longest tour length is minimal. In this work, we introduce the minimum idleness connectivity-constrained multi-robot patrolling problem, show that it is NP-hard, and model it as a mixed-integer linear program (MILP). The computational complexity of exactly solving this problem restrains practical applications, and therefore we develop approximate algorithms taking a solution for MMCCP as input. Our simulation experiments on 10 vertices and up to 3 robots compare the results of different solution approaches (including solving the MILP formulation) and show that our greedy algorithm can obtain an objective value close to the one of the MILP formulations but requires much less computation time. Experiments on instances with up to 100 vertices and 10 robots indicate that the greedy approximation algorithm tries to keep the length of the longest tour small by extending smaller tours for data exchange.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".