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Record W1588217500 · doi:10.37236/2639

Metric Dimension for Random Graphs

2013· article· en· W1588217500 on OpenAlexafffund
Béla Bollobás, Dieter Mitsche, Paweł Prałat

Bibliographic record

VenueThe Electronic Journal of Combinatorics · 2013
Typearticle
Languageen
FieldComputer Science
TopicGraph Labeling and Dimension Problems
Canadian institutionsToronto Metropolitan University
FundersNatural Sciences and Engineering Research Council of CanadaMicrosoft ResearchNational Science Foundation
KeywordsMetric dimensionCombinatoricsMathematicsVertex (graph theory)Dimension (graph theory)Packing dimensionGraphDiscrete mathematicsMetric (unit)Random graphMinkowski–Bouligand dimensionChordal graph1-planar graph

Abstract

fetched live from OpenAlex

The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$. In this paper we investigate the metric dimension of the random graph $G(n,p)$ for a wide range of probabilities $p=p(n)$.

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 machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.015
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.004
Threshold uncertainty score0.019

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.015
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.001
Bibliometrics0.0030.003
Science and technology studies0.0020.004
Scholarly communication0.0040.006
Open science0.0010.002
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0030.000

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.

Opus teacher head0.007
GPT teacher head0.215
Teacher spread0.208 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations39
Published2013
Admission routes2
Has abstractyes

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