Memory Requirements for Local Geometric Routing and Traversal in Digraphs
Bibliographic record
Abstract
Local route discovery in geometric, connected, undirected plane graphs is guaranteed by the Face Routing algorithm. The algorithm is local and geometric in the sense that it is executed by an agent moving along a network and using at each node only information about the current node (incl. its position) and a finite number of others (independent of graph size). Local geometric traversal algorithms also exist for undirected plane graphs. In this paper we show that no comparable routing or traversal algorithms exist for the class of strongly connected plane directed graphs (digraphs). We construct a class of digraphs embedded in the plane for which either local routing or local traversal requires Ω(n) memory bits, where n is the order of the graph. We discuss these results in light of finding a suitable model for mobile ad hoc networks with uni-directional edges, showing in the extended version of this paper that digraphs for which the Ω(n) lower bound holds occur even in the class of embedded digraphs arising out of a very conservative model. 1
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 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".