The emergence of sparse spanners and well-separated pair decomposition under anarchy
Bibliographic record
Abstract
A spanner graph on a set of points in Rd provides shortest paths between any pair of points with lengths at most a constant factor of their Euclidean distance. A spanner with a sparse set of edges is thus a good candidate for network backbones, as desired in many practical scenarios such as the transportation network and peer-to-peer network overlays. In this paper we investigate new models and aim to interpret why good spanners ‘emerge’ in reality, when they are clearly built in pieces by agents with their own interests and the construction is not coordinated. We show that the following algorithm of constructing an edge pq, if and only if there is no existing edge p′q′ with p′ and q′ at distances no more than (4(1+1/ε))-1·|pq| from p, qrespectively, generates a (1+ε)-spanner with a linear number of edges. The algorithm also implies a simple algorithm for constructing linear-size well-separated pair decompositions that may be of interest on their own. This new spanner construction algorithm has applications in the construction of nice network topologies for peer-to-peer systems, when peers join and leave the network and have only limited information about the rest of the network.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".