Lucas Fabian Naumann

Doctoral Student

Research

My research focuses on solving combinatorial optimization problems. In such a problem, you are given a number of interdependent decisions, and your task is to find a combination of decisions that yields an optimal outcome (or at least one that is good enough). The usually large number of decisions and their interdependence is what makes such problems (NP-)hard, and interesting to solve. A concrete example of a combinatorial optimization problem I am working on is correlation clustering. In correlation clustering, you are given a number of objects and pairwise (dis-)similarities between them, and your task is to cluster the objects such that similar ones are in the same cluster and dissimilar ones are in distinct clusters. A simple use case is the segmentation of an image by considering its pixels as the objects to be clustered and the (dis-)similarities between them to be their colour difference. However, there are various more sophisticated applications, such as object tracking, mapping neurites in 3D electron microscopy, and reconstructing particle interactions at the Large Hadron Collider. This general applicability is what makes this field so interesting to me: By studying one abstract mathematical problem, we obtain tools that can be used for a variety of downstream tasks. Another example of this is my current work on preprocessing the quadratic unconstrained binary optimization (QUBO) problem by identifying and fixing individual optimal decisions. QUBO is the mathematical language used to formulate problems on adiabatic quantum computers. By fixing certain optimal decisions in advance, they do not need to be modelled and searched for by the quantum computer. This reduces the number of qubits required and improves the quality of the solution.

Publications

Andres B., Irmai J. and Naumann L. F. Chorded cycle facets of the clique partitioning polytope. Discrete Applied Mathematics 378:662-670, 2026 (accepted)

@article{andres-2026-chorded,
    author = {Bjoern Andres and Jannik Irmai and Lucas Fabian Naumann},
    title = {Chorded cycle facets of the clique partitioning polytope},
    journal = {Discrete Applied Mathematics},
    year = {2026},
    volume = {378},
    pages = {662-670},
    doi = {10.1016/j.dam.2025.09.020},
}

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Naumann L. F., Irmai J. and Andres B. A Sub-Problem Quantum Alternating Operator Ansatz for Correlation Clustering. International Conference on Machine Learning (ICML) 2025

@inproceedings{naumann-2025-a,
    author = {Lucas Fabian Naumann 
        and Jannik Irmai 
        and Bjoern Andres},
    title = {},
    booktitle = {ICML},
    year = {2025},
    url = {https://proceedings.mlr.press/v267/naumann25a.html},
}

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Naumann L. F., Irmai J., Zhao S. and Andres B. Box Facets and Cut Facets of Lifted Multicut Polytopes. International Conference on Machine Learning (ICML) 2024

@inproceedings{naumann-2024-cut,
    author = {Lucas Fabian Naumann 
        and Jannik Irmai 
        and Shengxian Zhao 
        and Bjoern Andres},
    title = {Box Facets and Cut Facets of Lifted Multicut Polytopes},
    booktitle = {ICML},
    year = {2024},
    url = {https://proceedings.mlr.press/v235/naumann24a.html},
}

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Technical Reports

Irmai J., Naumann L. F. and Andres B. Graph Neural Networks with Triangle-Based Messages for the Multicut Problem. arXiv 2026

@misc{irmai-2026-graph,
      author = {Jannik Irmai and Lucas Fabian Naumann and Bjoern Andres},
      title = {Graph Neural Networks with Triangle-Based Messages for the Multicut Problem}, 
      year = {2026},
      eprint = {2605.13673},
      archivePrefix = {arXiv},
      primaryClass = {cs.LG},
      url = {https://arxiv.org/abs/2605.13673}, 
}

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