Bibliographic record
Abstract
Given an undirected and unweighted graph G, the subgraph S is an additive spanner of G with delay d if the distance between any two vertices in S is no more than d greater than their distance in G.It is known that the problem of finding additive spanners of arbitrary graphs for any fixed value of d with a minimum number of edges is NP-hard.Additive spanners are used as substructures for communication networks which are subject to design constraints such as minimizing the number of connections in the network, or permitting only a maximum number of connections at any one node.In this thesis, we consider the problem of constructing good additive spanners.We say that a spanner is "good" if it contains few edges, but not necessarily a minimum number of them.We present several algorithms which, given a graph G and a delay parameter d as input, produce a graph S which is an additive spanner of G with delay d.We evaluate each of these algorithms experimentally over a large set of input graphs, and for a series of delay values.We compare the spanners produced by each algorithm against each other, as well as against spanners produced by the best-known constructions for those graph classes with known additive spanner constructions.We highlight several algorithms which consistently produce spanners which are good with respect to the spanners produced by the other algorithms, and which are nearly as good as or, in some cases, better than the spanners produced by the constructions.Finally, we conclude with a discussion of future algorithmic approaches to the construction of additive spanners, as well as a list of possible applications for additive spanners beyond the realm of communication networks.To Stanley "Uncle Willie" Wilson, who knows a thing or two about experimentation.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".