Deterministic Collision-Free Exploration of Unknown Anonymous Graphs
Bibliographic record
Abstract
We consider the fundamental task of network exploration.A network is modeled as a simple connected undirected 𝑛-node graph with unlabeled nodes, and all ports at any node of degree 𝑑 are arbitrarily numbered 0, . . ., 𝑑 -1.Each of two identical mobile agents, initially situated at distinct nodes, has to visit all nodes and stop.Agents execute the same deterministic algorithm and move in synchronous rounds: in each round an agent can either remain at the same node or move to an adjacent node.Exploration must be collision-free: in every round at most one agent can be at any node.We assume that agents have vision of radius 2: an awake agent situated at a node 𝑣 can see the subgraph induced by all nodes at distance at most 2 from 𝑣, sees all port numbers in this subgraph and the agents located at these nodes.Agents do not know the entire graph but they know an upper bound 𝑛 on its size.The time of an exploration is the number of rounds since the wakeup of the later agent to the termination by both agents.We show a collisionfree exploration algorithm working in time polynomial in 𝑛, for arbitrary graphs of size larger than 2. Moreover we show that if agents have only vision of radius 1, then collision-free exploration is impossible, e.g., in any tree of diameter 2.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".