On Delivery Guarantees and Worst-Case Forwarding Bounds of Elementary Face Routing Components in Ad Hoc and Sensor Networks
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Bibliographic record
Abstract
In this paper, we provide a thorough theoretical study on delivery guarantees, loop-free operation, and worst-case behavior of face and combined greedy-face routing. We show that under specific planar topology control schemes, recovery from a greedy routing failure is always possible without changing between any adjacent faces. Guaranteed delivery then follows from guaranteed recovery while traversing the very first face. In arbitrary planar graphs, however, a proper face selection mechanism is of importance since recovery from a greedy routing failure may require visiting a sequence of faces before greedy routing can be restarted again. We provide complete and formal proofs that several proposed face routing and combined greedy-face routing schemes guarantee message delivery in specific planar graph classes or even in arbitrary planar graphs. We also discuss the reasons why other methods fail to deliver a message or even end up in a loop. In addition, we investigate the behavior of face routing in arbitrary not necessarily planar networks and show, while delivery guarantees cannot be supported in such a general case, most face and combined greedy-face routing variants support at least loop-free operation. For those variants, we derive worst-case upper bounds on the number of forwarding steps.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it