---
license: mit
task_categories:
- graph-ml
---

# RandSATBench: Benchmarks for Constraint Satisfaction Problems

This repository contains the benchmarks presented in the paper [Benchmarking Graph Neural Networks in Solving Hard Constraint Satisfaction Problems](https://huggingface.co/papers/2602.18419).

**RandSATBench** provides a mixed set of easy, hard, and unsatisfiable instances of constraint satisfaction problems, specifically *q-coloring* and *Boolean satisfiability* (K-SAT) problems. The goal is to provide a challenging setting to compare the performance of deep learning methods (particularly Graph Neural Networks) against classical exact and heuristic solvers.

- **Paper:** [https://huggingface.co/papers/2602.18419](https://huggingface.co/papers/2602.18419)
- **Repository:** [https://github.com/ArtLabBocconi/RandCSPBench](https://github.com/ArtLabBocconi/RandCSPBench)

## Datasets

The benchmark includes datasets for Boolean satisfiability (3-SAT and 4-SAT) and coloring problems (3-coloring and 5-coloring). The instances vary in size ($N=16, 32, 64, 256$) and connectivity.

| Dataset | # Train Instances | # Test Instances |
|---------|-------------------|------------------|
| 3-SAT   | 168,000           | 42,000           | 
| 4-SAT   | 84,000            | 21,000           | 
| 3-col   | 60,000            | 20,000           | 
| 5-col   | 60,000            | 20,000           | 

## Usage

### K-SAT

The random instances of 3-SAT or 5-SAT problems in CNF format can be downloaded using the following:

```bash
wget https://huggingface.co/datasets/CarloLucibello/kSAT-Benchmarks/resolve/main/kSAT.zip
unzip kSAT.zip
```

Ground truth solutions obtained by running the CaDiCal solver are available in the corresponding `train_labels.csv` files.

### q-coloring

To generate the random graphs for the 3-coloring and 5-coloring benchmarks, use the scripts provided in the GitHub repository:

```bash
cd datasets
python gen_graphs_coloring.py
```

## Citation

If you use this benchmark in your research, please cite:

```bibtex
@article{lucibello2026benchmarking,
  title={Benchmarking Graph Neural Networks in Solving Hard Constraint Satisfaction Problems},
  author={Lucibello, Carlo and others},
  journal={arXiv preprint arXiv:2602.18419},
  year={2026}
}
```