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Record W100499361

Static symmetry breaking in circle packing

2010· article· en· W100499361 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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueCologne Twente Workshop on Graphs and Combinatorial Optimization · 2010
Typearticle
Languageen
FieldEngineering
TopicOptimization and Packing Problems
Canadian institutionsHEC Montréal
Fundersnot available
KeywordsCircle packingSquare (algebra)RADIUSPacking problemsSymmetry breakingCombinatoricsUnit squareSymmetry (geometry)Unit (ring theory)MathematicsUnit circleWork (physics)PhysicsGeometryComputer scienceQuantum mechanics
DOInot available

Abstract

fetched live from OpenAlex

1 IntroductionWe present new Static Symmetry-Breaking Inequalities (SSBI) [11,6] for theproblem of packing equal circles in a square [9]. The new SSBIs provide amarked computational improvement with respect to past work [1], though notyet at the level where a purely Mathematical Programming (MP) based spatialBranch-and-Bound (sBB) can be competitive with a Branch-and-Bound (BB)“boosted” by combinatorial and geometrical devices such as [9]. We considerthe following formulation of Circle Packing in a Square (CPS) problem:given N ∈ N and L ∈ N, can N non-overlapping circles of unit radius be ar-ranged in a square of side 2L? This is equivalent to the more usual formulationwhere one maximizes the number of non-overlapping circles of unit radius in asquare of side 2L with L ∈ Q

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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: Simulation or modeling
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.083
Threshold uncertainty score0.922

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
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 head0.007
GPT teacher head0.218
Teacher spread0.212 · 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