Capacity Provisioning a Valiant Load-Balanced Network
Bibliographic record
Abstract
Valiant load balancing (VLB), also called two-stage load balancing, is gaining popularity as a routing scheme that can serve arbitrary traffic matrices. To date, VLB network design is well understood on a logical full-mesh topology, where VLB is optimal even when nodes can fail. In this paper, we address the design and capacity provisioning of arbitrary VLB network topologies. First, we introduce an algorithm to determine if VLB can serve all traffic matrices when a fixed number of arbitrary links fail, and we show how to find a min-cost expansion of the network - via link upgrades and installs - so that it is resilient to these failures. Additionally, we propose a method to design a new VLB network under the fixed-charge network design cost model. Finally, we prove that VLB is no longer optimal on unrestricted topologies, and can require more capacity than shortest path routing to serve all traffic matrices on some topologies. These results rely on a novel theorem that characterizes the capacity VLB requires of links crossing each cut, i.e., a partition, of the network's 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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".