Using Lagrangian Relaxation for Radio Resource Allocation in High Altitude Platforms
Bibliographic record
Abstract
In this paper, we study radio resource allocation for multicasting in OFDMA based high altitude platforms (HAPs). We formulate and solve an optimization problem that finds the best allocation of HAP resources such as radio power, sub-channels, and time slots. The problem also finds the best possible frequency reuse across the cells that constitute the service area of the HAP. The objective is to maximize the number of user terminals that receive the requested multicast streams in the HAP service area in a given OFDMA frame. A bounding subroutine in a branch and bound algorithm can be obtained by decomposing it into two easier subproblems, due to its high complexity, and solving them iteratively. Subproblem 1 turns out to be a binary integer linear program of no explicitly noticeable structure and therefore Lagrangian relaxation is used to dualize some constraints to get a structure that is easy to solve. Subproblem 2 turns out to be a linear program with a continuous knapsack problem structure. Hence a greedy algorithm is proposed to solve subproblem 2 to optimality. The subgradient method is used to solve for the dual variables in the dual problem to get the tightest bounds.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".