On Multi-round Sensor Deployment for Barrier Coverage
Bibliographic record
Abstract
We consider the k-barrier coverage problem, that is, the problem of deploying sensors on a border or perimeter to ensure that any intruder would be detected by at least k sensors. With random deployment of sensors, there is always a chance of gaps in coverage, thereby necessitating multiple rounds of deployment. In this paper, we study multi-round wireless sensor deployment on a border modeled as a line segment. We present two different classes of deployment strategies: complete and partial. In complete strategies, in every round, sensors are deployed over the entire border segment, while in partial strategies, sensors are deployed over only some part(s) of the border. First, we analyze the probability of k-coverage for any complete strategy as a function of parameters such as length of barrier to be covered, the width of the intruder, the sensing range of sensors, as well as the density of deployed sensors. Second, we propose two specific deployment strategies - Fixed-Density Complete and Fixed-Density Partial - and analyze the expected number of deployment rounds and expected total number of deployed sensors for each strategy. Next, we present a model for cost analysis of multi-round sensor deployment and calculate, for each deployment strategy, the expected total cost as a function of problem parameters and density of sensor deployment. Finally we find the optimal density of sensors in each round that minimizes the total expected cost of deployment for each deployment strategy. We validate our analysis by extensive simulation results.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".