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
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".