TRADE-OFFS BETWEEN LOAD AND DEGREE IN VIRTUAL PATH LAYOUTS
Bibliographic record
Abstract
We study virtual path layouts in ATM networks. Packets are routed along virtual paths in the network by maintaining a routing field whose subfields determine intermediate destinations of the packet, i.e., the endpoints of virtual paths on its way to the final destination. Most of the research on virtual path layouts has focused on tradeoffs between load (i.e., the maximum number of virtual paths passing through a link) and the hop number of the layout (i.e., the maximum number of virtual paths needed to travel between any two nodes). There is however another important limitation on construction of layouts, resulting from technological properties of switches situated at nodes. This bound is the degree of the layout (i.e., the maximum number of virtual paths with a common endpoint). In this paper we study relations between these three parameters of virtual path layouts, for the all-to-all problem. For any integer h, we show tradeoffs between load and degree of h-hop layouts in the ring and in the mesh by establishing upper and lower bounds on these parameters. Our bounds on the degree of an h-hop layout of given load are asymptotically tight and the bounds on the load of an h-hop layout of given degree are asymptotically tight for constant h.
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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 | 0.027 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".