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Documents authored by Maas, Nikolai

Artifact
Software
DOI: 10.4230/artifacts.26212
Mt-KaHyPar

Authors: Tobias Heuer, Lars Gottesbüren, Nikolai Maas, and Simeon Schrape

Abstract
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Tobias Heuer, Lars Gottesbüren, Nikolai Maas, Simeon Schrape. Mt-KaHyPar (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{dagstuhl-artifact-26212,
   title = {{Mt-KaHyPar}}, 
   author = {Heuer, Tobias and Gottesb\"{u}ren, Lars and Maas, Nikolai and Schrape, Simeon},
   note = {Software, version 1.5.3., swhId: \href{https://archive.softwareheritage.org/swh:1:dir:0285e232ceaf8b004e75d01d1e5f4e6984770663;origin=https://github.com/kahypar/mt-kahypar;visit=swh:1:snp:c52ed946227f7476ef4ddbf78f09bb757c686d87;anchor=swh:1:rev:6d12d9cf210390624f3757e9b5399469d2d2ae68}{\texttt{swh:1:dir:0285e232ceaf8b004e75d01d1e5f4e6984770663}} (visited on 2026-06-15)},
   url = {https://github.com/kahypar/mt-kahypar/tree/sea2026},
   doi = {10.4230/artifacts.26212},
}
Document
DOI: 10.4230/LIPIcs.SEA.2026.25
Engineering Learned Heuristics to Improve Clustering for Multilevel Graph Partitioning

Authors: Simeon Schrape, Nikolai Maas, Kenneth Langedal, and Daniel Seemaier

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
Balanced Graph Partitioning is a classical optimization problem where quality guarantees are computationally infeasible, and practical solvers therefore rely on manually engineered heuristics. Yet, the problem has also proven difficult for approaches that rely heavily on machine learning - especially since applications often need to partition graphs of huge scale in a short amount of time. Instead, we demonstrate how to achieve practical improvements with a more careful approach that uses machine learning to improve heuristic decisions within the state-of-the-art solver Mt-KaHyPar. We use a pre-trained neural network to predict a score for each edge, which then guides clustering decisions in the first phase of the partitioning (the coarsening). Combined with corresponding adjustments to the clustering algorithm and an efficient implementation of the neural network logic, we improve the overall solution quality while preserving the efficiency and scalability of the original algorithm. Our detailed evaluation on more than 180 graphs shows an average quality improvement of 2% on a class of graphs with beneficial properties, and unchanged quality on all remaining graphs. Moreover, our improvements generalize to a set of instances from the literature that are much larger than the graphs used during training.
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Simeon Schrape, Nikolai Maas, Kenneth Langedal, and Daniel Seemaier. Engineering Learned Heuristics to Improve Clustering for Multilevel Graph Partitioning. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 25:1-25:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{schrape_et_al:LIPIcs.SEA.2026.25,
  author =	{Schrape, Simeon and Maas, Nikolai and Langedal, Kenneth and Seemaier, Daniel},
  title =	{{Engineering Learned Heuristics to Improve Clustering for Multilevel Graph Partitioning}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{25:1--25:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.25},
  URN =		{urn:nbn:de:0030-drops-260295},
  doi =		{10.4230/LIPIcs.SEA.2026.25},
  annote =	{Keywords: Graph Partitioning, Graph Algorithms, Machine Learning, Neural Networks}
}
Artifact
Software
DOI: 10.4230/artifacts.24666
KaMinPar

Authors: Lars Gottesbüren, Nikolai Maas, Dominik Rosch, Peter Sanders, and Daniel Seemaier

Abstract
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Lars Gottesbüren, Nikolai Maas, Dominik Rosch, Peter Sanders, Daniel Seemaier. KaMinPar (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-24666,
   title = {{KaMinPar}}, 
   author = {Gottesb\"{u}ren, Lars and Maas, Nikolai and Rosch, Dominik and Sanders, Peter and Seemaier, Daniel},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:2ec38dbccb676136f71dc1796d6a06b450c48c6d}{\texttt{swh:1:dir:2ec38dbccb676136f71dc1796d6a06b450c48c6d}} (visited on 2025-10-01)},
   url = {https://github.com/KaHIP/KaMinPar/commit/73eeaa2371c6826e166c9ca1383996f14d8c7a2a},
   doi = {10.4230/artifacts.24666},
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.32
Linear-Time Multilevel Graph Partitioning via Edge Sparsification

Authors: Lars Gottesbüren, Nikolai Maas, Dominik Rosch, Peter Sanders, and Daniel Seemaier

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate how to achieve the best of both worlds with a linear time multilevel algorithm. Multilevel algorithms construct a hierarchy of increasingly smaller graphs by repeatedly contracting clusters of nodes. Our approach preserves their distinct advantage, allowing refinement of the partition over multiple levels with increasing detail. At the same time, we use edge sparsification to guarantee geometric size reduction between the levels and thus linear running time. We provide a proof of the linear running time as well as additional insights into the behavior of multilevel algorithms, showing that graphs with low modularity are most likely to trigger worst-case running time. We evaluate multiple approaches for edge sparsification and integrate our algorithm into the state-of-the-art multilevel partitioner KaMinPar, maintaining its excellent parallel scalability. As demonstrated in detailed experiments, this results in a 1.49× average speedup (up to 4× for some instances) with only 1% loss in solution quality. Moreover, our algorithm clearly outperforms state-of-the-art single-level and streaming approaches.
Cite as

Lars Gottesbüren, Nikolai Maas, Dominik Rosch, Peter Sanders, and Daniel Seemaier. Linear-Time Multilevel Graph Partitioning via Edge Sparsification. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gottesburen_et_al:LIPIcs.ESA.2025.32,
  author =	{Gottesb\"{u}ren, Lars and Maas, Nikolai and Rosch, Dominik and Sanders, Peter and Seemaier, Daniel},
  title =	{{Linear-Time Multilevel Graph Partitioning via Edge Sparsification}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.32},
  URN =		{urn:nbn:de:0030-drops-245007},
  doi =		{10.4230/LIPIcs.ESA.2025.32},
  annote =	{Keywords: Graph Partitioning, Graph Algorithms, Linear Time Algorithms, Graph Sparsification}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.8
Multilevel Hypergraph Partitioning with Vertex Weights Revisited

Authors: Tobias Heuer, Nikolai Maas, and Sebastian Schlag

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Abstract
The balanced hypergraph partitioning problem (HGP) is to partition the vertex set of a hypergraph into k disjoint blocks of bounded weight, while minimizing an objective function defined on the hyperedges. Whereas real-world applications often use vertex and edge weights to accurately model the underlying problem, the HGP research community commonly works with unweighted instances. In this paper, we argue that, in the presence of vertex weights, current balance constraint definitions either yield infeasible partitioning problems or allow unnecessarily large imbalances and propose a new definition that overcomes these problems. We show that state-of-the-art hypergraph partitioners often struggle considerably with weighted instances and tight balance constraints (even with our new balance definition). Thus, we present a recursive-bipartitioning technique that is able to reliably compute balanced (and hence feasible) solutions. The proposed method balances the partition by pre-assigning a small subset of the heaviest vertices to the two blocks of each bipartition (using an algorithm originally developed for the job scheduling problem) and optimizes the actual partitioning objective on the remaining vertices. We integrate our algorithm into the multilevel hypergraph partitioner KaHyPar and show that our approach is able to compute balanced partitions of high quality on a diverse set of benchmark instances.
Cite as

Tobias Heuer, Nikolai Maas, and Sebastian Schlag. Multilevel Hypergraph Partitioning with Vertex Weights Revisited. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{heuer_et_al:LIPIcs.SEA.2021.8,
  author =	{Heuer, Tobias and Maas, Nikolai and Schlag, Sebastian},
  title =	{{Multilevel Hypergraph Partitioning with Vertex Weights Revisited}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.8},
  URN =		{urn:nbn:de:0030-drops-137802},
  doi =		{10.4230/LIPIcs.SEA.2021.8},
  annote =	{Keywords: multilevel hypergraph partitioning, balanced partitioning, vertex weights}
}
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