Exact graph decomposition algorithms for MaxClique and Minimum Vertex Cover problems. The aim of this project is to create graph decomposition algorithms for specific problems, which generate sub-problems that are small enough to be able to be solved on modern quantum annealers.

DBK in DBK.py performs graph decomposition for the Maximum Clique problem.

DBR in DBR.py performs graph decomposition for the Minimum Vertex Cover problem.

Each of these functions use a user specified solver function. In order to validate the correctness of the algorithm, we can use an exact solver function. The purpose of these algorithms is to use a quantum annealer as the solver.

validate_DBK.py imports DBK and validates the algorithm using the exact solver provided in the networkx package

validate_DBR.py does the same except with DBR

@inproceedings{pelofske2019solving,
  title={Solving large maximum clique problems on a quantum annealer},
  author={Pelofske, Elijah and Hahn, Georg and Djidjev, Hristo},
  booktitle={International Workshop on Quantum Technology and Optimization Problems},
  pages={123--135},
  year={2019},
  organization={Springer}
}

@inproceedings{pelofske2019solving,
  title={Solving large minimum vertex cover problems on a quantum annealer},
  author={Pelofske, Elijah and Hahn, Georg and Djidjev, Hristo},
  booktitle={Proceedings of the 16th ACM International Conference on Computing Frontiers},
  pages={76--84},
  year={2019}
}

@article{pelofske2021decomposition,
  title={Decomposition algorithms for solving NP-hard problems on a quantum annealer},
  author={Pelofske, Elijah and Hahn, Georg and Djidjev, Hristo},
  journal={Journal of Signal Processing Systems},
  volume={93},
  number={4},
  pages={405--420},
  year={2021},
  publisher={Springer}
}

• Elijah Pelofske: Information Sciences, Los Alamos National Laboratory
• Georg Hahn: T.H. Chan School of Public Health, Harvard University
• Hristo Djidjev: Information Sciences, Los Alamos National Laboratory

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