MétaCan
Menu
Back to cohort
Record W2738777098 · doi:10.1137/1.9781611975031.136

Testing Bounded Arboricity

2018· preprint· en· W2738777098 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueSociety for Industrial and Applied Mathematics eBooks · 2018
Typepreprint
Languageen
FieldComputer Science
TopicComplexity and Algorithms in Graphs
Canadian institutionsnot available
FundersH2020 European Research CouncilAzrieli FoundationUnited States-Israel Binational Science FoundationNational Science Foundation
KeywordsArboricityCombinatoricsBounded functionTreewidthMathematicsOmegaDense graphDegree (music)Upper and lower boundsPlanar graphGraphDiscrete mathematicsBinary logarithm1-planar graphPathwidthChordal graphPhysicsLine graph

Abstract

fetched live from OpenAlex

In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs with bounded treewidth) and randomly generated preferential attachment graphs. Graphs with bounded arboricity have been studied extensively in the past, in particular since for many problems they allow for much more efficient algorithms and/or better approximation ratios. We present a tolerant tester in the sparse-graphs model. The sparse-graphs model allows access to degree queries and neighbor queries, and the distance is defined with respect to the actual number of edges. More specifically, our algorithm distinguishes between graphs that are e-close to having arboricity α and graphs that c · ∊-far from having arboricity 3α, where c is an absolute small constant. The query complexity and running time of the algorithm are1 where n denotes the number of vertices and m denotes the number of edges. In terms of the dependence on n and m this bound is optimal up to poly-logarithmic factors since queries are necessary (and the arboricity of a graph is always . We leave it as an open question whether the dependence on 1/∊ can be improved from quasi-polynomial to polynomial. Our techniques include an efficient local simulation for approximating the outcome of a global (almost) forest-decomposition algorithm as well as a tailored procedure of edge sampling.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.072
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0010.000
Scholarly communication0.0010.000
Open science0.0010.002
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0000.000

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 head0.136
GPT teacher head0.281
Teacher spread0.145 · 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