Solving binary and continuous knapsack problems for radio resource allocation over High Altitude Platforms
Bibliographic record
Abstract
In this paper, radio resource allocation for multicasting in OFDMA based High Altitude Platforms is considered. An optimization problem for the model described in the paper is formulated which turns out to be a Mixed Integer Non-Linear Program. Due to its high complexity, we use Lagrangian relaxation to dualize some constraint sets. The Lagrangian relaxed problem is then decomposed into two Lagrangian subproblems, one is a binary knapsack Lagrangian subproblem (BKLSP) and the other is continuous knapsack Lagrangian subproblem (CKLSP). The BKLSP is responsible for the assignment of the OFDMA subchannels and time slots to multicast sessions as well as user assignment to the multicast groups in a particular frame. The CKLSP is responsible for HAP power allocation to multicast sessions in the HAP service area. The two subproblems can be solved iteratively in search for a better solution, if there is any, for the Lagrangian problem. For the BKLSP we use two different solution algorithms, one based on dynamic programming and the other is a greedy algorithm. A greedy algorithm is also used for the CKLSP. The entire approach can be used to obtain bounds in a branch and bound algorithm for each of its nodes.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".