4 Search Results for "Lamm, Sebastian"

Document
DOI: 10.4230/LIPIcs.SEA.2024.4
Separator Based Data Reduction for the Maximum Cut Problem

Authors: Jonas Charfreitag, Christine Dahn, Michael Kaibel, Philip Mayer, Petra Mutzel, and Lukas Schürmann

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Preprocessing is an important ingredient for solving the maximum cut problem to optimality on real-world graphs. In our work, we derive a new framework for data reduction rules based on vertex separators. Vertex separators are sets of vertices, whose removal increases the number of connected components of a graph. Certain small separators can be found in linear time, allowing for an efficient combination of our framework with existing data reduction rules. Additionally, we complement known data reduction rules for triangles with a new one. In our computational experiments on established benchmark instances, we clearly show the effectiveness and efficiency of our proposed data reduction techniques. The resulting graphs are significantly smaller than in earlier studies and sometimes no vertex is left, so preprocessing has fully solved the instance to optimality. The introduced techniques are also shown to offer significant speedup potential for an exact state-of-the-art solver and to help a state-of-the-art heuristic to produce solutions of higher quality.
Cite as

Jonas Charfreitag, Christine Dahn, Michael Kaibel, Philip Mayer, Petra Mutzel, and Lukas Schürmann. Separator Based Data Reduction for the Maximum Cut Problem. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{charfreitag_et_al:LIPIcs.SEA.2024.4,
  author =	{Charfreitag, Jonas and Dahn, Christine and Kaibel, Michael and Mayer, Philip and Mutzel, Petra and Sch\"{u}rmann, Lukas},
  title =	{{Separator Based Data Reduction for the Maximum Cut Problem}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{4:1--4:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.4},
  URN =		{urn:nbn:de:0030-drops-203698},
  doi =		{10.4230/LIPIcs.SEA.2024.4},
  annote =	{Keywords: Data Reduction, Maximum Cut, Vertex Separators}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.5
Buffered Streaming Edge Partitioning

Authors: Adil Chhabra, Marcelo Fonseca Faraj, Christian Schulz, and Daniel Seemaier

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Addressing the challenges of processing massive graphs, which are prevalent in diverse fields such as social, biological, and technical networks, we introduce HeiStreamE and FreightE, two innovative (buffered) streaming algorithms designed for efficient edge partitioning of large-scale graphs. HeiStreamE utilizes an adapted Split-and-Connect graph model and a Fennel-based multilevel partitioning scheme, while FreightE partitions a hypergraph representation of the input graph. Besides ensuring superior solution quality, these approaches also overcome the limitations of existing algorithms by maintaining linear dependency on the graph size in both time and memory complexity with no dependence on the number of blocks of partition. Our comprehensive experimental analysis demonstrates that HeiStreamE outperforms current streaming algorithms and the re-streaming algorithm 2PS in partitioning quality (replication factor), and is more memory-efficient for real-world networks where the number of edges is far greater than the number of vertices. Further, FreightE is shown to produce fast and efficient partitions, particularly for higher numbers of partition blocks.
Cite as

Adil Chhabra, Marcelo Fonseca Faraj, Christian Schulz, and Daniel Seemaier. Buffered Streaming Edge Partitioning. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chhabra_et_al:LIPIcs.SEA.2024.5,
  author =	{Chhabra, Adil and Fonseca Faraj, Marcelo and Schulz, Christian and Seemaier, Daniel},
  title =	{{Buffered Streaming Edge Partitioning}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.5},
  URN =		{urn:nbn:de:0030-drops-203701},
  doi =		{10.4230/LIPIcs.SEA.2024.5},
  annote =	{Keywords: graph partitioning, edge partitioning, streaming, online, buffered partitioning}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.20
Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks

Authors: Kenneth Langedal, Demian Hespe, and Peter Sanders

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Identifying a maximum independent set is a fundamental NP-hard problem. This problem has several real-world applications and requires finding the largest possible set of vertices not adjacent to each other in an undirected graph. Over the past few years, branch-and-bound and branch-and-reduce algorithms have emerged as some of the most effective methods for solving the problem exactly. Specifically, the branch-and-reduce approach, which combines branch-and-bound principles with reduction rules, has proven particularly successful in tackling previously unmanageable real-world instances. This progress was largely made possible by the development of more effective reduction rules. Nevertheless, other key components that can impact the efficiency of these algorithms have not received the same level of interest. Among these is the branching strategy, which determines which vertex to branch on next. Until recently, the most widely used strategy was to choose the vertex of the highest degree. In this work, we present a graph neural network approach for selecting the next branching vertex. The intricate nature of current branch-and-bound solvers makes supervised and reinforcement learning difficult. Therefore, we use a population-based genetic algorithm to evolve the model’s parameters instead. Our proposed approach results in a speedup on 73% of the benchmark instances with a median speedup of 24%.
Cite as

Kenneth Langedal, Demian Hespe, and Peter Sanders. Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{langedal_et_al:LIPIcs.SEA.2024.20,
  author =	{Langedal, Kenneth and Hespe, Demian and Sanders, Peter},
  title =	{{Targeted Branching for the Maximum Independent Set Problem Using Graph Neural Networks}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.20},
  URN =		{urn:nbn:de:0030-drops-203853},
  doi =		{10.4230/LIPIcs.SEA.2024.20},
  annote =	{Keywords: Graphs, Independent Set, Vertex Cover, Graph Neural Networks, Branch-and-Reduce}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.17
Targeted Branching for the Maximum Independent Set Problem

Authors: Demian Hespe, Sebastian Lamm, and Christian Schorr

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

Abstract
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. In recent years, some of the most successful algorithms for solving this problem are based on the branch-and-bound or branch-and-reduce paradigms. In particular, branch-and-reduce algorithms, which combine branch-and-bound with reduction rules, have been able to achieve substantial results, solving many previously infeasible real-world instances. These results were to a large part achieved by developing new, more practical reduction rules. However, other components that have been shown to have a significant impact on the performance of these algorithms have not received as much attention. One of these is the branching strategy, which determines what vertex is included or excluded in a potential solution. Even now, the most commonly used strategy selects vertices solely based on their degree and does not take into account other factors that contribute to the performance of the algorithm. In this work, we develop and evaluate several novel branching strategies for both branch-and-bound and branch-and-reduce algorithms. Our strategies are based on one of two approaches which are motivated by existing research. They either (1) aim to decompose the graph into two or more connected components which can then be solved independently, or (2) try to remove vertices that hinder the application of a reduction rule which can lead to smaller graphs. Our experimental evaluation on a large set of real-world instances indicates that our strategies are able to improve the performance of the state-of-the-art branch-and-reduce algorithm by Akiba and Iwata. To be more specific, our reduction-based packing branching rule is able to outperform the default branching strategy of selecting a vertex of highest degree on 65% of all instances tested. Furthermore, our decomposition-based strategy based on edge cuts is able to achieve a speedup of 2.29 on sparse networks (1.22 on all instances).
Cite as

Demian Hespe, Sebastian Lamm, and Christian Schorr. Targeted Branching for the Maximum Independent Set Problem. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hespe_et_al:LIPIcs.SEA.2021.17,
  author =	{Hespe, Demian and Lamm, Sebastian and Schorr, Christian},
  title =	{{Targeted Branching for the Maximum Independent Set Problem}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{17:1--17:21},
  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.2021.17},
  URN =		{urn:nbn:de:0030-drops-137893},
  doi =		{10.4230/LIPIcs.SEA.2021.17},
  annote =	{Keywords: Graphs, Combinatorial Optimization, Independent Set, Vertex Cover, Clique, Branch-and-Reduce, Branch-and-Bound, Data Reduction}
}
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