A Branch-and-Cut Approach for the Minimum-Energy Broadcasting Problem in Wireless Networks
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Bibliographic record
Abstract
This paper studies the minimum-energy broadcasting problem (MEBP) in wireless sensor networks. The aim of the MEBP is to determine the power assignment of each node in a wireless sensor network such that a specified source node can broadcast messages to each of the other nodes and the total energy consumption is minimized. We first present a new formulation involving an exponential number of constraints for the broadcasting requirement. We then prove that under a mild condition, these constraints for the broadcasting requirement are facet defining. Directly using the proposed formulation, we further present a new branch-and-cut (B&C) solution approach to optimally solve the MEBP. We propose three ways to identify violated cuts at each node in the enumeration tree. Finally, we test the proposed B&C approach on 1,000 randomly generated instances with different properties and compare it with other alternative methods in the literature. Computational results demonstrate the effectiveness and efficiency of our approach using the proposed formulation for instances with up to 100 nodes.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it