Bibliographic record
Abstract
Recent advances in network coding research dramatically changed the underlying structure of optimal multicast routing algorithms and made them efficiently computable. While most such algorithm design assumes a single file/layer being multicast, layered coding introduces new challenges into the paradigm due to its cumulative decoding nature. Layered coding is designed to handle heterogeneity in receiver capacities, and a node may decode layer k only if it successfully receives all layers in 1.. k . We show that recently proposed optimization models for layered multicast do not correctly address this challenge. We argue that in order to achieve the absolute maximum throughput (or minimum cost), it is necessary to decouple the application-layer throughput from network-layer throughput. In particular, a node should be able to receive a nonconsecutive layer or a partial layer even if it cannot decode and utilize it (e.g., for playback in media streaming applications). The rationale is that nodes at critical network locations need to receive data just for helping other peers. We present a mathematical programming model that addresses these challenges and achieves absolute optimal performance. Simulation results show considerable throughput gain (cost reduction) compared with previous models, in a broad range of network scenarios. We then provide a formal proof that the layered multicast problem is NP-complete. We design a randomized rounding algorithm to approximate the optimal layered multicast, and show the efficacy of our technique using simulations. We then proceed to further generalize our model by studying the optimal progression of layer sizes. We show that such optimization is nonconvex, and apply a simulated annealing algorithm to solve it, with flexible trade-off between solution quality and running time. We verify the effectiveness of the new model and the simulated annealing algorithm through extensive simulations, and point out insights on the connection between optimal layer size progression and node capacity distribution.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".