Algorithms for stochastic optimization of multicast content delivery with network coding
Bibliographic record
Abstract
The usage of network resources by content providers is commonly governed by Service-Level Agreements (SLA) between the content provider and the network service provider. Resource usage exceeding the limits specified in the SLA incurs the content provider additional charges, usually at a higher cost. Hence, the content provider's goal is to provision adequate resources in the SLA based on forecasts of future demand. We study capacity purchasing strategies when the content provider employs network coded multicast as the media delivery mechanism, with uncertainty in its future customer set explicitly taken into consideration. The latter requires the content provider to make capacity provisioning decisions based on market predictions and historical customer usage patterns. The probabilistic element suggests a stochastic optimization approach. We model this problem as a two-stage stochastic optimization problem with recourse. Such optimizations are #P-hard to solve directly, and we design two approximation algorithms for them. The first is a heuristic algorithm that exploits properties unique to network coding, so that only polynomial-time operations are needed. It performs well in general scenarios, but the gap from the optimal solution is not bounded by any constant in the worst case. This motivates our second approach, a sampling algorithm partly inspired from the work of Gupta et al. [2004a]. We employ techniques from duality theory in linear optimization to prove that the sampling algorithm provides a 3-approximation to the stochastic multicast problem. We conduct extensive simulations to illustrate the efficacy of both algorithms, and show that the performance of both is usually within 10% of the optimal solution in practice.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".