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Record W2620834784

Variable Space Search for Graph Coloring

2006· article· fr· W2620834784 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

VenueArchive ouverte UNIGE (University of Geneva) · 2006
Typearticle
Languagefr
FieldDecision Sciences
TopicScheduling and Timetabling Solutions
Canadian institutionsPolytechnique Montréal
Fundersnot available
KeywordsMathematicsGraph coloringComplete coloringFractional coloringCombinatoricsEdge coloringVertex (graph theory)Local search (optimization)Best-first searchSpace (punctuation)List coloringGraphSearch algorithmDiscrete mathematicsBeam searchAlgorithmComputer scienceGraph powerLine graph
DOInot available

Abstract

fetched live from OpenAlex

Let G = (V,E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1,..., k}) to each vertex of G so that no edge has both endpoints with the same color. We present a new local search algorithm, called Variable Space Search (VSS), which we apply to the k-coloring problem. VSS extends the Formulation Space Search (FSS) methodology by considering sev-eral non equivalent formulations of a same problem, each one being associated with a set of neighborhoods and an objective function. The search moves from one formulation to another when it is blocked at a local optimum with a given formulation. The k-coloring problem is thus solved by combining different formulations of the problem which are not equivalent, in the sense that some constraints are possibly re-laxed in one search space and always satisfied in another. We show that the proposed algorithm improves on every local search used inde-pendently (i.e., with a unique search space), and is competitive with the currently best coloring methods, which are complex hybrid evolu-tionary algorithms. 1

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)0.002
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: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.598
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.002
Science and technology studies0.0010.001
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.000

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 head0.054
GPT teacher head0.281
Teacher spread0.226 · 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