Notice: This website is continuously updated as new conference proceedings and journal volumes are published. Consequently, the figures presented here may differ from those reported in our publications.
A brief overview of our methodology is provided on the Methods page, along with references to publications documenting our approach and links to the code and data used in each study.
The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates.
Power Iterated Color Refinement
Authors: Kristian Kersting, Martin Mladenov, Roman Garnett, Martin Grohe
AAAI 2014 | Venue PDF | LLM Run Details | Input Tokens: 16,877 Total number of tokens sent to the LLM as input for this paper's analysis. | Output Tokens: 4,291 Total number of tokens produced by the LLM (including reasoning/thinking tokens) for this paper's analysis.
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We support our theoretical results with experiments on real-world graphs with millions of edges. |
| Researcher Affiliation | Academia | Kristian Kersting TU Dortmund University {fn.ln}@cs.tu-dortmund.de Martin Mladenov TU Dortmund University {fn.ln}@cs.tu-dortmund.de Roman Garnett University of Bonn EMAIL Martin Grohe RWTH Aachen EMAIL |
| Pseudocode | Yes | Algorithm 1: CGCR(A): CG for Color Refinement; Algorithm 2: COLORS(M); Algorithm 3: CHARACTMAT(M); Algorithm 4: CGCR(A): CG for Color Refinement; Algorithm 5: HCGCR(A): Hashed CGCR; Algorithm 6: PICGCR(A): Power Iterated CGCR |
| Open Source Code | Yes | we implemented naive versions of CGCR, HCGCR (denoted as Hashing and available at https://github.com/rmgarnett/fast_wl/) and PICGCR in Matlab |
| Open Datasets | Yes | Table 1: Scaling results on graphs generated from http://www.cise.ufl.edu/research/sparse/matrices/index.html (matrices were turned into graphs using A := A + AT and thresholding |A| > 0). |
| Dataset Splits | No | The paper does not specify validation splits or detailed train/validation/test partitioning for the datasets used in experiments. |
| Hardware Specification | Yes | on a single Linux machine( 4 3.4 GHz cores, 32 GB main memory) |
| Software Dependencies | No | we implemented naive versions of CGCR, HCGCR (...) and PICGCR in Matlab. Matlab version number is not specified. |
| Experiment Setup | Yes | The convergence threshold ϵ for PI was set to 10 8 and the damping factor α to 0.95. The maximum number of PI iterations was set to 500 (denoted as PIfix) resp. to min(2k, τ) (PIflex). |