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Documents authored by Schulz, Christian

Artifact
Software
DOI: 10.4230/artifacts.24670
Implementation of our dynamic algorithm for minimum orientation

Authors: Ernestine Grossmann, Henrik Reinstädtler, Eva Rotenberg, Christian Schulz, Ivor van der Hoog, and Juliette Vlieghe

Abstract
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Ernestine Grossmann, Henrik Reinstädtler, Eva Rotenberg, Christian Schulz, Ivor van der Hoog, Juliette Vlieghe. Implementation of our dynamic algorithm for minimum orientation (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-24670,
   title = {{Implementation of our dynamic algorithm for minimum orientation}}, 
   author = {Grossmann, Ernestine and Reinst\"{a}dtler, Henrik and Rotenberg, Eva and Schulz, Christian and van der Hoog, Ivor and Vlieghe, Juliette},
   note = {Software, Villum Fonden VIL37507, DFG SCHU 2567/8-1, Marie Skłodowska-Curie 899987, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:0ea52feafca9f6d8ce3ee893686fde2510513e9e;origin=https://github.com/DynGraphLab/DynDeltaApprox;visit=swh:1:snp:d75d11daa88538aaa86297daef487996502d243b;anchor=swh:1:rev:f8c3028a966664ce26b0f32c08de00dec2103127}{\texttt{swh:1:dir:0ea52feafca9f6d8ce3ee893686fde2510513e9e}} (visited on 2025-10-01)},
   url = {https://github.com/DynGraphLab/DynDeltaApprox},
   doi = {10.4230/artifacts.24670},
}
Artifact
Software
DOI: 10.4230/artifacts.24674
HeiHGM/Streaming

Authors: Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz

Abstract
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Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, Christian Schulz. HeiHGM/Streaming (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-24674,
   title = {{HeiHGM/Streaming}}, 
   author = {Reinst\"{a}dtler, Henrik and Ferdous, S M and Pothen, Alex and U\c{c}ar, Bora and Schulz, Christian},
   note = {Software, DFG-SCHU 2567/8-1, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:4e4522550296fb38202457ce7371bf7034ae45d9;origin=https://github.com/HeiHGM/Streaming;visit=swh:1:snp:981431da5340cbbf116e22fe0896634c2d164c50;anchor=swh:1:rev:acc7c88e5544a70f356db838f4027629ae8ffb4b}{\texttt{swh:1:dir:4e4522550296fb38202457ce7371bf7034ae45d9}} (visited on 2025-10-01)},
   url = {https://github.com/HeiHGM/Streaming},
   doi = {10.4230/artifacts.24674},
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.65
From Theory to Practice: Engineering Approximation Algorithms for Dynamic Orientation

Authors: Ernestine Grossmann, Henrik Reinstädtler, Eva Rotenberg, Christian Schulz, Ivor van der Hoog, and Juliette Vlieghe

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

Abstract
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed approximation algorithms for dynamically maintaining graph orientations. We comprehensively describe the underlying data structures, including efficient bucketing techniques and round-robin updates. Our implementation has a natural parameter λ, which allows for a trade-off between algorithmic efficiency and the quality of the solution. In the extensive experimental evaluation, we demonstrate that our implementation offers a considerable speedup. Using different quality metrics, we show that our implementations are very competitive and can outperform previous methods. Overall, our approach solves more instances than other methods while being up to 112 times faster on instances that are solvable by all methods compared.
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Ernestine Grossmann, Henrik Reinstädtler, Eva Rotenberg, Christian Schulz, Ivor van der Hoog, and Juliette Vlieghe. From Theory to Practice: Engineering Approximation Algorithms for Dynamic Orientation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 65:1-65:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grossmann_et_al:LIPIcs.ESA.2025.65,
  author =	{Grossmann, Ernestine and Reinst\"{a}dtler, Henrik and Rotenberg, Eva and Schulz, Christian and van der Hoog, Ivor and Vlieghe, Juliette},
  title =	{{From Theory to Practice: Engineering Approximation Algorithms for Dynamic Orientation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{65:1--65:18},
  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.2025.65},
  URN =		{urn:nbn:de:0030-drops-245331},
  doi =		{10.4230/LIPIcs.ESA.2025.65},
  annote =	{Keywords: Dynamic graphs, out-orientation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.79
Semi-Streaming Algorithms for Hypergraph Matching

Authors: Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz

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

Abstract
We propose two one-pass streaming algorithms for the NP-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an approximation guarantee of 1/(d(1+ε)) and requires 𝒪((n/ε)log²n) bits of memory, where n is the number of vertices in the hypergraph, d is the maximum number of vertices in a hyperedge, and ε > 0 is a parameter to be chosen. The second algorithm computes, stores, and updates a single matching as the edges stream, with an approximation ratio dependent on a parameter α. Its best approximation guarantee is 1/((2d-1) + 2 √{d(d-1)}), and it requires only 𝒪(n) memory. We have implemented both algorithms and compared them with respect to solution quality, memory consumption, and running times on two diverse sets of hypergraphs with a non-streaming greedy and a naive streaming algorithm. Our results show that the streaming algorithms achieve much better solution quality than naive algorithms when facing adverse orderings. Furthermore, these algorithms reduce the memory required by a factor of 13 in the geometric mean on our test problems, and also outperform the offline Greedy algorithm in running time.
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Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz. Semi-Streaming Algorithms for Hypergraph Matching. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{reinstadtler_et_al:LIPIcs.ESA.2025.79,
  author =	{Reinst\"{a}dtler, Henrik and Ferdous, S M and Pothen, Alex and U\c{c}ar, Bora and Schulz, Christian},
  title =	{{Semi-Streaming Algorithms for Hypergraph Matching}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{79:1--79:19},
  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.2025.79},
  URN =		{urn:nbn:de:0030-drops-245478},
  doi =		{10.4230/LIPIcs.ESA.2025.79},
  annote =	{Keywords: hypergraph, matching, semi-streaming}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.11
CluStRE: Streaming Graph Clustering with Multi-Stage Refinement

Authors: Adil Chhabra, Shai Dorian Peretz, and Christian Schulz

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
We present CluStRE, a novel streaming graph clustering algorithm that balances computational efficiency with high-quality clustering using multi-stage refinement. Unlike traditional in-memory clustering approaches, CluStRE processes graphs in a streaming setting, significantly reducing memory overhead while leveraging re-streaming and evolutionary heuristics to improve solution quality. Our method dynamically constructs a quotient graph, enabling modularity-based optimization while efficiently handling large-scale graphs. We introduce multiple configurations of CluStRE to provide trade-offs between speed, memory consumption, and clustering quality. Experimental evaluations demonstrate that CluStRE improves solution quality by 89.8%, operates 2.6× faster, and uses less than two-thirds of the memory required by the state-of-the-art streaming clustering algorithm on average. Moreover, our strongest mode enhances solution quality by up to 150% on average. With this, CluStRE achieves comparable solution quality to in-memory algorithms, i.e. over 96% of the quality of clustering approaches, including Louvain, effectively bridging the gap between streaming and traditional clustering methods.
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Adil Chhabra, Shai Dorian Peretz, and Christian Schulz. CluStRE: Streaming Graph Clustering with Multi-Stage Refinement. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chhabra_et_al:LIPIcs.SEA.2025.11,
  author =	{Chhabra, Adil and Dorian Peretz, Shai and Schulz, Christian},
  title =	{{CluStRE: Streaming Graph Clustering with Multi-Stage Refinement}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.11},
  URN =		{urn:nbn:de:0030-drops-232493},
  doi =		{10.4230/LIPIcs.SEA.2025.11},
  annote =	{Keywords: graph clustering, community, streaming, online, memetic, evolutionary}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.22
Concurrent Iterated Local Search for the Maximum Weight Independent Set Problem

Authors: Ernestine Großmann, Kenneth Langedal, and Christian Schulz

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with the highest possible weight under the constraint that no two vertices in the set can share an edge. This work presents a new iterated local search heuristic called CHILS (Concurrent Hybrid Iterated Local Search). The implementation of CHILS is specifically designed to handle large graphs of varying densities. CHILS outperforms the current state-of-the-art on commonly used benchmark instances, especially on the largest instances. As an added benefit, CHILS can run in parallel to leverage the power of multicore processors. The general technique used in CHILS is a new concurrent metaheuristic called Concurrent Difference-Core Heuristic that can also be applied to other combinatorial problems.
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Ernestine Großmann, Kenneth Langedal, and Christian Schulz. Concurrent Iterated Local Search for the Maximum Weight Independent Set Problem. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gromann_et_al:LIPIcs.SEA.2025.22,
  author =	{Gro{\ss}mann, Ernestine and Langedal, Kenneth and Schulz, Christian},
  title =	{{Concurrent Iterated Local Search for the Maximum Weight Independent Set Problem}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.22},
  URN =		{urn:nbn:de:0030-drops-232600},
  doi =		{10.4230/LIPIcs.SEA.2025.22},
  annote =	{Keywords: Randomized Local Search, Heuristics, Maximum Weight Independent Set, Algorithm Engineering, Parallel Computing}
}
Artifact
Software
DOI: 10.4230/artifacts.22501
HeiOrient

Authors: Henrik Reinstädtler, Christian Schulz, and Bora Uçar

Abstract
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Henrik Reinstädtler, Christian Schulz, Bora Uçar. HeiOrient (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22501,
   title = {{HeiOrient}}, 
   author = {Reinst\"{a}dtler, Henrik and Schulz, Christian and U\c{c}ar, Bora},
   note = {Software, DFG-SCHU 2567/3-1, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:be7317d125554a54dfd1c9d17521c500c4e1ebc3;origin=https://github.com/HeiOrient/HeiOrient;visit=swh:1:snp:ad428689c405e27808a6eac12433782b1de2166e;anchor=swh:1:rev:830c983f61d5199a6b6b0daab77fddf55d158cfd}{\texttt{swh:1:dir:be7317d125554a54dfd1c9d17521c500c4e1ebc3}} (visited on 2024-11-28)},
   url = {https://github.com/HeiOrient/HeiOrient},
   doi = {10.4230/artifacts.22501},
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.97
Engineering Edge Orientation Algorithms

Authors: Henrik Reinstädtler, Christian Schulz, and Bora Uçar

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out-degree of a vertex in the resulting directed graph. This problem, which is solvable in polynomial time, arises in many applications. An ongoing challenge in edge orientation algorithms is their scalability, particularly in handling large-scale networks with millions or billions of edges efficiently. We propose a novel algorithmic framework based on finding and manipulating simple paths to face this challenge. Our framework is based on an existing algorithm and allows many algorithmic choices. By carefully exploring these choices and engineering the underlying algorithms, we obtain an implementation which is more efficient and scalable than the current state-of-the-art. Our experiments demonstrate significant performance improvements compared to state-of-the-art solvers. On average our algorithm is 6.59 times faster when compared to the state-of-the-art.
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Henrik Reinstädtler, Christian Schulz, and Bora Uçar. Engineering Edge Orientation Algorithms. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 97:1-97:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{reinstadtler_et_al:LIPIcs.ESA.2024.97,
  author =	{Reinst\"{a}dtler, Henrik and Schulz, Christian and U\c{c}ar, Bora},
  title =	{{Engineering Edge Orientation Algorithms}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{97:1--97:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.97},
  URN =		{urn:nbn:de:0030-drops-211682},
  doi =		{10.4230/LIPIcs.ESA.2024.97},
  annote =	{Keywords: edge orientation, pseudoarboricity, graph algorithms}
}
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.
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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.2024.11
Engineering Weighted Connectivity Augmentation Algorithms

Authors: Marcelo Fonseca Faraj, Ernestine Großmann, Felix Joos, Thomas Möller, and Christian Schulz

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

Abstract
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find a minimum cost subset of a given set of weighted links that increases the connectivity of a graph by one when the links are added to the edge set of the input instance. In this work, we give a first implementation of recently discovered better-than-2 approximations. Furthermore, we propose three new heuristics and one exact approach. These include a greedy algorithm considering link costs and the number of unique cuts covered, an approach based on minimum spanning trees and a local search algorithm that may improve a given solution by swapping links of paths. Our exact approach uses an ILP formulation with efficient cut enumeration as well as a fast initialization routine. We then perform an extensive experimental evaluation which shows that our algorithms are faster and yield the best solutions compared to the current state-of-the-art as well as the recently discovered better-than-2 approximation algorithms. Our novel local search algorithm can improve solution quality even further.
Cite as

Marcelo Fonseca Faraj, Ernestine Großmann, Felix Joos, Thomas Möller, and Christian Schulz. Engineering Weighted Connectivity Augmentation Algorithms. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{faraj_et_al:LIPIcs.SEA.2024.11,
  author =	{Faraj, Marcelo Fonseca and Gro{\ss}mann, Ernestine and Joos, Felix and M\"{o}ller, Thomas and Schulz, Christian},
  title =	{{Engineering Weighted Connectivity Augmentation Algorithms}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{11:1--11:22},
  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.2024.11},
  URN =		{urn:nbn:de:0030-drops-203768},
  doi =		{10.4230/LIPIcs.SEA.2024.11},
  annote =	{Keywords: weighted connectivity augmentation, approximation, heuristic, integer linear program, algorithm engineering}
}
Document
DOI: 10.4230/DagRep.13.8.1
Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)

Authors: George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman

Published in: Dagstuhl Reports, Volume 13, Issue 8 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23331 "Recent Trends in Graph Decomposition", which took place from 13. August to 18. August, 2023. The seminar brought together 33 experts from academia and industry to discuss graph decomposition, a pivotal technique for handling massive graphs in applications such as social networks and scientific simulations. The seminar addressed the challenges posed by contemporary hardware designs, the potential of deep neural networks and reinforcement learning in developing heuristics, the unique optimization requirements of large sparse data, and the need for scalable algorithms suitable for emerging architectures. Through presentations, discussions, and collaborative sessions, the event fostered an exchange of innovative ideas, leading to the creation of community notes highlighting key open problems in the field.
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George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman. Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331). In Dagstuhl Reports, Volume 13, Issue 8, pp. 1-45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{karypis_et_al:DagRep.13.8.1,
  author =	{Karypis, George and Schulz, Christian and Strash, Darren and Ajwani, Deepak and Bisseling, Rob H. and Casel, Katrin and \c{C}ataly\"{u}rek, \"{U}mit V. and Chevalier, C\'{e}dric and Chudigiewitsch, Florian and Faraj, Marcelo Fonseca and Fellows, Michael and Gottesb\"{u}ren, Lars and Heuer, Tobias and Kaya, Kamer and Lacki, Jakub and Langguth, Johannes and Li, Xiaoye Sherry and Mayer, Ruben and Meintrup, Johannes and Mizutani, Yosuke and Pellegrini, Fran\c{c}ois and Petrini, Fabrizio and Rosamond, Frances and Safro, Ilya and Schlag, Sebastian and Sharma, Roohani and Sullivan, Blair D. and U\c{c}ar, Bora and Yzelman, Albert-Jan},
  title =	{{Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)}},
  pages =	{1--45},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{8},
  editor =	{Karypis, George and Schulz, Christian and Strash, Darren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.8.1},
  URN =		{urn:nbn:de:0030-drops-198114},
  doi =		{10.4230/DagRep.13.8.1},
  annote =	{Keywords: combinatorial optimization, experimental algorithmics, parallel algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.34
Faster Local Motif Clustering via Maximum Flows

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

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Local clustering aims to identify a cluster within a given graph that includes a designated seed node or a significant portion of a group of seed nodes. This cluster should be well-characterized, i.e., it has a high number of internal edges and a low number of external edges. In this work, we propose SOCIAL, a novel algorithm for local motif clustering which optimizes for motif conductance based on a local hypergraph model representation of the problem and an adapted version of the max-flow quotient-cut improvement algorithm (MQI). In our experiments with the triangle motif, SOCIAL produces local clusters with an average motif conductance 1.7% lower than the state-of-the-art, while being up to multiple orders of magnitude faster.
Cite as

Adil Chhabra, Marcelo Fonseca Faraj, and Christian Schulz. Faster Local Motif Clustering via Maximum Flows. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chhabra_et_al:LIPIcs.ESA.2023.34,
  author =	{Chhabra, Adil and Fonseca Faraj, Marcelo and Schulz, Christian},
  title =	{{Faster Local Motif Clustering via Maximum Flows}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.34},
  URN =		{urn:nbn:de:0030-drops-186871},
  doi =		{10.4230/LIPIcs.ESA.2023.34},
  annote =	{Keywords: local motif clustering, motif conductance, maximum flows, max-flow quotient-cut improvement}
}
Document
DOI: 10.4230/LIPIcs.SEA.2023.15
FREIGHT: Fast Streaming Hypergraph Partitioning

Authors: Kamal Eyubov, Marcelo Fonseca Faraj, and Christian Schulz

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
Partitioning the vertices of a (hyper)graph into k roughly balanced blocks such that few (hyper)edges run between blocks is a key problem for large-scale distributed processing. A current trend for partitioning huge (hyper)graphs using low computational resources are streaming algorithms. In this work, we propose FREIGHT: a Fast stREamInG Hypergraph parTitioning algorithm which is an adaptation of the widely-known graph-based algorithm Fennel. By using an efficient data structure, we make the overall running of FREIGHT linearly dependent on the pin-count of the hypergraph and the memory consumption linearly dependent on the numbers of nets and blocks. The results of our extensive experimentation showcase the promising performance of FREIGHT as a highly efficient and effective solution for streaming hypergraph partitioning. Our algorithm demonstrates competitive running time with the Hashing algorithm, with a difference of a maximum factor of four observed on three fourths of the instances. Significantly, our findings highlight the superiority of FREIGHT over all existing (buffered) streaming algorithms and even the in-memory algorithm HYPE, with respect to both cut-net and connectivity measures. This indicates that our proposed algorithm is a promising hypergraph partitioning tool to tackle the challenge posed by large-scale and dynamic data processing.
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Kamal Eyubov, Marcelo Fonseca Faraj, and Christian Schulz. FREIGHT: Fast Streaming Hypergraph Partitioning. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{eyubov_et_al:LIPIcs.SEA.2023.15,
  author =	{Eyubov, Kamal and Fonseca Faraj, Marcelo and Schulz, Christian},
  title =	{{FREIGHT: Fast Streaming Hypergraph Partitioning}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.15},
  URN =		{urn:nbn:de:0030-drops-183657},
  doi =		{10.4230/LIPIcs.SEA.2023.15},
  annote =	{Keywords: Hypergraph partitioning, graph partitioning, edge partitioning, streaming}
}
Document
DOI: 10.4230/LIPIcs.SEA.2023.16
Arc-Flags Meet Trip-Based Public Transit Routing

Authors: Ernestine Großmann, Jonas Sauer, Christian Schulz, and Patrick Steil

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
We present Arc-Flag TB, a journey planning algorithm for public transit networks which combines Trip-Based Public Transit Routing (TB) with the Arc-Flags speedup technique. Compared to previous attempts to apply Arc-Flags to public transit networks, which saw limited success, our approach uses stronger pruning rules to reduce the search space. Our experiments show that Arc-Flag TB achieves a speedup of up to two orders of magnitude over TB, offering query times of less than a millisecond even on large countrywide networks. Compared to the state-of-the-art speedup technique Trip-Based Public Transit Routing Using Condensed Search Trees (TB-CST), our algorithm achieves similar query times but requires significantly less additional memory. Other state-of-the-art algorithms which achieve even faster query times, e.g., Public Transit Labeling, require enormous memory usage. In contrast, Arc-Flag TB offers a tradeoff between query performance and memory usage due to the fact that the number of regions in the network partition required by our algorithm is a configurable parameter. We also identify a previously undiscovered issue in the transfer precomputation of TB, which causes both TB-CST and Arc-Flag TB to answer some queries incorrectly. We provide discussion on how to resolve this issue in the future. Currently, Arc-Flag TB answers 1-6% of queries incorrectly, compared to over 20% for TB-CST on some networks.
Cite as

Ernestine Großmann, Jonas Sauer, Christian Schulz, and Patrick Steil. Arc-Flags Meet Trip-Based Public Transit Routing. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gromann_et_al:LIPIcs.SEA.2023.16,
  author =	{Gro{\ss}mann, Ernestine and Sauer, Jonas and Schulz, Christian and Steil, Patrick},
  title =	{{Arc-Flags Meet Trip-Based Public Transit Routing}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.16},
  URN =		{urn:nbn:de:0030-drops-183664},
  doi =		{10.4230/LIPIcs.SEA.2023.16},
  annote =	{Keywords: Public transit routing, graph algorithms, algorithm engineering}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.26
The PACE 2022 Parameterized Algorithms and Computational Experiments Challenge: Directed Feedback Vertex Set

Authors: Ernestine Großmann, Tobias Heuer, Christian Schulz, and Darren Strash

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
The Parameterized Algorithms and Computational Experiments challenge (PACE) 2022 was devoted to engineer algorithms solving the NP-hard Directed Feedback Vertex Set (DFVS) problem. The DFVS problem is to find a minimum subset X ⊆ V in a given directed graph G = (V,E) such that, when all vertices of X and their adjacent edges are deleted from G, the remainder is acyclic. Overall, the challenge had 90 participants from 26 teams, 12 countries, and 3 continents that submitted their implementations to this year’s competition. In this report, we briefly describe the setup of the challenge, the selection of benchmark instances, as well as the ranking of the participating teams. We also briefly outline the approaches used in the submitted solvers.
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Ernestine Großmann, Tobias Heuer, Christian Schulz, and Darren Strash. The PACE 2022 Parameterized Algorithms and Computational Experiments Challenge: Directed Feedback Vertex Set. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gromann_et_al:LIPIcs.IPEC.2022.26,
  author =	{Gro{\ss}mann, Ernestine and Heuer, Tobias and Schulz, Christian and Strash, Darren},
  title =	{{The PACE 2022 Parameterized Algorithms and Computational Experiments Challenge: Directed Feedback Vertex Set}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.26},
  URN =		{urn:nbn:de:0030-drops-173826},
  doi =		{10.4230/LIPIcs.IPEC.2022.26},
  annote =	{Keywords: Feedback Vertex Set, Algorithm Engineering, FPT, Kernelization, Heuristics}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.SEA.2022
LIPIcs, Volume 233, SEA 2022, Complete Volume

Authors: Christian Schulz and Bora Uçar

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
LIPIcs, Volume 233, SEA 2022, Complete Volume
Cite as

20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 1-434, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{schulz_et_al:LIPIcs.SEA.2022,
  title =	{{LIPIcs, Volume 233, SEA 2022, Complete Volume}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{1--434},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022},
  URN =		{urn:nbn:de:0030-drops-165331},
  doi =		{10.4230/LIPIcs.SEA.2022},
  annote =	{Keywords: LIPIcs, Volume 233, SEA 2022, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.SEA.2022.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Christian Schulz and Bora Uçar

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{schulz_et_al:LIPIcs.SEA.2022.0,
  author =	{Schulz, Christian and U\c{c}ar, Bora},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.0},
  URN =		{urn:nbn:de:0030-drops-165342},
  doi =		{10.4230/LIPIcs.SEA.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SAND.2022.1
Recent Advances in Fully Dynamic Graph Algorithms (Invited Talk)

Authors: Kathrin Hanauer, Monika Henzinger, and Christian Schulz

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.
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Kathrin Hanauer, Monika Henzinger, and Christian Schulz. Recent Advances in Fully Dynamic Graph Algorithms (Invited Talk). In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 1:1-1:47, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hanauer_et_al:LIPIcs.SAND.2022.1,
  author =	{Hanauer, Kathrin and Henzinger, Monika and Schulz, Christian},
  title =	{{Recent Advances in Fully Dynamic Graph Algorithms}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{1:1--1:47},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.1},
  URN =		{urn:nbn:de:0030-drops-159434},
  doi =		{10.4230/LIPIcs.SAND.2022.1},
  annote =	{Keywords: fully dynamic graph algorithms, survey}
}
Document
DOI: 10.4230/LIPIcs.CSL.2022.24
Decidability for Sturmian Words

Authors: Philipp Hieronymi, Dun Ma, Reed Oei, Luke Schaeffer, Christian Schulz, and Jeffrey Shallit

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract
We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable. Using a general adder recognizing addition in Ostrowski numeration systems by Baranwal, Schaeffer and Shallit, we prove that the first-order expansions of Presburger arithmetic by a single Sturmian word are uniformly ω-automatic, and then deduce the decidability of the theory of the class of such structures. Using an implementation of this decision algorithm called Pecan, we automatically reprove classical theorems about Sturmian words in seconds, and are able to obtain new results about antisquares and antipalindromes in characteristic Sturmian words.
Cite as

Philipp Hieronymi, Dun Ma, Reed Oei, Luke Schaeffer, Christian Schulz, and Jeffrey Shallit. Decidability for Sturmian Words. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 24:1-24:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hieronymi_et_al:LIPIcs.CSL.2022.24,
  author =	{Hieronymi, Philipp and Ma, Dun and Oei, Reed and Schaeffer, Luke and Schulz, Christian and Shallit, Jeffrey},
  title =	{{Decidability for Sturmian Words}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{24:1--24:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.24},
  URN =		{urn:nbn:de:0030-drops-157440},
  doi =		{10.4230/LIPIcs.CSL.2022.24},
  annote =	{Keywords: Decidability, Sturmian words, Ostrowski numeration systems, Automated theorem proving}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.48
Deep Multilevel Graph Partitioning

Authors: Lars Gottesbüren, Tobias Heuer, Peter Sanders, Christian Schulz, and Daniel Seemaier

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that require parallel processing. While the amount of available cores in parallel architectures has significantly increased in recent years, state-of-the-art graph partitioning algorithms do not work well if the input needs to be partitioned into a large number of blocks. Often currently available algorithms compute highly imbalanced solutions, solutions of low quality, or have excessive running time for this case. This is due to the fact that most high-quality general-purpose graph partitioners are multilevel algorithms which perform graph coarsening to build a hierarchy of graphs, initial partitioning to compute an initial solution, and local improvement to improve the solution throughout the hierarchy. However, for large number of blocks, the smallest graph in the hierarchy that is used for initial partitioning still has to be large. In this work, we substantially mitigate these problems by introducing deep multilevel graph partitioning and a shared-memory implementation thereof. Our scheme continues the multilevel approach deep into initial partitioning - integrating it into a framework where recursive bipartitioning and direct k-way partitioning are combined such that they can operate with high performance and quality. Our integrated approach is stronger, more flexible, arguably more elegant, and reduces bottlenecks for parallelization compared to existing multilevel approaches. For example, for large number of blocks our algorithm is on average at least an order of magnitude faster than competing algorithms while computing partitions with comparable solution quality. At the same time, our algorithm consistently produces balanced solutions. Moreover, for small number of blocks, our algorithms are the fastest among competing systems with comparable quality.
Cite as

Lars Gottesbüren, Tobias Heuer, Peter Sanders, Christian Schulz, and Daniel Seemaier. Deep Multilevel Graph Partitioning. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 48:1-48:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gottesburen_et_al:LIPIcs.ESA.2021.48,
  author =	{Gottesb\"{u}ren, Lars and Heuer, Tobias and Sanders, Peter and Schulz, Christian and Seemaier, Daniel},
  title =	{{Deep Multilevel Graph Partitioning}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{48:1--48:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.48},
  URN =		{urn:nbn:de:0030-drops-146298},
  doi =		{10.4230/LIPIcs.ESA.2021.48},
  annote =	{Keywords: graph partitioning, graph algorithms, multilevel, shared-memory, parallel}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.13
O'Reach: Even Faster Reachability in Large Graphs

Authors: Kathrin Hanauer, Christian Schulz, and Jonathan Trummer

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

Abstract
One of the most fundamental problems in computer science is the reachability problem: Given a directed graph and two vertices s and t, can s reach t via a path? We revisit existing techniques and combine them with new approaches to support a large portion of reachability queries in constant time using a linear-sized reachability index. Our new algorithm O'Reach can be easily combined with previously developed solutions for the problem or run standalone. In a detailed experimental study, we compare a variety of algorithms with respect to their index-building and query times as well as their memory footprint on a diverse set of instances. Our experiments indicate that the query performance often depends strongly not only on the type of graph, but also on the result, i.e., reachable or unreachable. Furthermore, we show that previous algorithms are significantly sped up when combined with our new approach in almost all scenarios. Surprisingly, due to cache effects, a higher investment in space doesn't necessarily pay off: Reachability queries can often be answered even faster than single memory accesses in a precomputed full reachability matrix.
Cite as

Kathrin Hanauer, Christian Schulz, and Jonathan Trummer. O'Reach: Even Faster Reachability in Large Graphs. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 13:1-13:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hanauer_et_al:LIPIcs.SEA.2021.13,
  author =	{Hanauer, Kathrin and Schulz, Christian and Trummer, Jonathan},
  title =	{{O'Reach: Even Faster Reachability in Large Graphs}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{13:1--13:24},
  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.2021.13},
  URN =		{urn:nbn:de:0030-drops-137856},
  doi =		{10.4230/LIPIcs.SEA.2021.13},
  annote =	{Keywords: Reachability, Static Graphs, Graph Algorithms, Reachability Index, Algorithm Engineering}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.58
Dynamic Matching Algorithms in Practice

Authors: Monika Henzinger, Shahbaz Khan, Richard Paul, and Christian Schulz

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
In recent years, significant advances have been made in the design and analysis of fully dynamic maximal matching algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. In this paper, we attempt to bridge the gap between theory and practice that is currently observed for the fully dynamic maximal matching problem. We engineer several algorithms and empirically study those algorithms on an extensive set of dynamic instances.
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Monika Henzinger, Shahbaz Khan, Richard Paul, and Christian Schulz. Dynamic Matching Algorithms in Practice. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2020.58,
  author =	{Henzinger, Monika and Khan, Shahbaz and Paul, Richard and Schulz, Christian},
  title =	{{Dynamic Matching Algorithms in Practice}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{58:1--58:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.58},
  URN =		{urn:nbn:de:0030-drops-129243},
  doi =		{10.4230/LIPIcs.ESA.2020.58},
  annote =	{Keywords: Matching, Dynamic Matching, Blossom Algorithm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.59
Finding All Global Minimum Cuts in Practice

Authors: Monika Henzinger, Alexander Noe, Christian Schulz, and Darren Strash

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs. Our algorithm uses a multitude of kernelization rules to reduce the graph to a small equivalent instance and then finds all minimum cuts using an optimized version of the algorithm of Nagamochi, Nakao and Ibaraki. In shared memory we are able to find all minimum cuts of graphs with up to billions of edges and millions of minimum cuts in a few minutes. We also give a new linear time algorithm to find the most balanced minimum cuts given as input the representation of all minimum cuts.
Cite as

Monika Henzinger, Alexander Noe, Christian Schulz, and Darren Strash. Finding All Global Minimum Cuts in Practice. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2020.59,
  author =	{Henzinger, Monika and Noe, Alexander and Schulz, Christian and Strash, Darren},
  title =	{{Finding All Global Minimum Cuts in Practice}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{59:1--59:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.59},
  URN =		{urn:nbn:de:0030-drops-129255},
  doi =		{10.4230/LIPIcs.ESA.2020.59},
  annote =	{Keywords: Minimum Cut, Graph Algorithm, Algorithm Engineering, Cut Enumeration, Balanced Cut, Global Minimum Cut, Large-scale Graph Analysis}
}
Document
DOI: 10.4230/LIPIcs.SEA.2020.4
High-Quality Hierarchical Process Mapping

Authors: Marcelo Fonseca Faraj, Alexander van der Grinten, Henning Meyerhenke, Jesper Larsson Träff, and Christian Schulz

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known, an important task is then to map the blocks of the partition onto the processors such that the overall communication cost is reduced. We present novel multilevel algorithms that integrate graph partitioning and process mapping. Important ingredients of our algorithm include fast label propagation, more localized local search, initial partitioning, as well as a compressed data structure to compute processor distances without storing a distance matrix. Moreover, our algorithms are able to exploit a given hierarchical structure of the distributed system under consideration. Experiments indicate that our algorithms speed up the overall mapping process and, due to the integrated multilevel approach, also find much better solutions in practice. For example, one configuration of our algorithm yields similar solution quality as the previous state-of-the-art in terms of mapping quality for large numbers of partitions while being a factor 9.3 faster. Compared to the currently fastest iterated multilevel mapping algorithm Scotch, we obtain 16% better solutions while investing slightly more running time.
Cite as

Marcelo Fonseca Faraj, Alexander van der Grinten, Henning Meyerhenke, Jesper Larsson Träff, and Christian Schulz. High-Quality Hierarchical Process Mapping. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{faraj_et_al:LIPIcs.SEA.2020.4,
  author =	{Faraj, Marcelo Fonseca and van der Grinten, Alexander and Meyerhenke, Henning and Tr\"{a}ff, Jesper Larsson and Schulz, Christian},
  title =	{{High-Quality Hierarchical Process Mapping}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.4},
  URN =		{urn:nbn:de:0030-drops-120782},
  doi =		{10.4230/LIPIcs.SEA.2020.4},
  annote =	{Keywords: Process Mapping, Graph Partitioning, Algorithm Engineering}
}
Document
DOI: 10.4230/LIPIcs.SEA.2020.14
Faster Fully Dynamic Transitive Closure in Practice

Authors: Kathrin Hanauer, Monika Henzinger, and Christian Schulz

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been thoroughly investigated in theory and many specialized algorithms for solving it have been proposed in the last decades. In two large studies [Frigioni ea, 2001; Krommidas and Zaroliagis, 2008], a number of these algorithms have been evaluated experimentally against simple, static algorithms for graph traversal, showing the competitiveness and even superiority of the simple algorithms in practice, except for very dense random graphs or very high ratios of queries. A major drawback of those studies is that only small and mostly randomly generated graphs are considered. In this paper, we engineer new algorithms to maintain all-pairs reachability information which are simple and space-efficient. Moreover, we perform an extensive experimental evaluation on both generated and real-world instances that are several orders of magnitude larger than those in the previous studies. Our results indicate that our new algorithms outperform all state-of-the-art algorithms on all types of input considerably in practice.
Cite as

Kathrin Hanauer, Monika Henzinger, and Christian Schulz. Faster Fully Dynamic Transitive Closure in Practice. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hanauer_et_al:LIPIcs.SEA.2020.14,
  author =	{Hanauer, Kathrin and Henzinger, Monika and Schulz, Christian},
  title =	{{Faster Fully Dynamic Transitive Closure in Practice}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.14},
  URN =		{urn:nbn:de:0030-drops-120887},
  doi =		{10.4230/LIPIcs.SEA.2020.14},
  annote =	{Keywords: Dynamic Graph Algorithms, Reachability, Transitive Closure}
}
Document
DOI: 10.4230/LIPIcs.SEA.2018.3
Memetic Graph Clustering

Authors: Sonja Biedermann, Monika Henzinger, Christian Schulz, and Bernhard Schuster

Published in: LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

Abstract
It is common knowledge that there is no single best strategy for graph clustering, which justifies a plethora of existing approaches. In this paper, we present a general memetic algorithm, VieClus, to tackle the graph clustering problem. This algorithm can be adapted to optimize different objective functions. A key component of our contribution are natural recombine operators that employ ensemble clusterings as well as multi-level techniques. Lastly, we combine these techniques with a scalable communication protocol, producing a system that is able to compute high-quality solutions in a short amount of time. We instantiate our scheme with local search for modularity and show that our algorithm successfully improves or reproduces all entries of the 10th DIMACS implementation challenge under consideration using a small amount of time.
Cite as

Sonja Biedermann, Monika Henzinger, Christian Schulz, and Bernhard Schuster. Memetic Graph Clustering. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{biedermann_et_al:LIPIcs.SEA.2018.3,
  author =	{Biedermann, Sonja and Henzinger, Monika and Schulz, Christian and Schuster, Bernhard},
  title =	{{Memetic Graph Clustering}},
  booktitle =	{17th International Symposium on Experimental Algorithms (SEA 2018)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-070-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{103},
  editor =	{D'Angelo, Gianlorenzo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.3},
  URN =		{urn:nbn:de:0030-drops-89389},
  doi =		{10.4230/LIPIcs.SEA.2018.3},
  annote =	{Keywords: Graph Clustering, Evolutionary Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2018.4
ILP-based Local Search for Graph Partitioning

Authors: Alexandra Henzinger, Alexander Noe, and Christian Schulz

Published in: LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

Abstract
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that solve the partitioning problem to optimality. However, since those programs typically do not scale to large inputs, we adapt them to heuristically improve a given partition. We do so by defining a much smaller model that allows us to use symmetry breaking and other techniques that make the approach scalable. For example, in Walshaw's well-known benchmark tables we are able to improve roughly half of all entries when the number of blocks is high.
Cite as

Alexandra Henzinger, Alexander Noe, and Christian Schulz. ILP-based Local Search for Graph Partitioning. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{henzinger_et_al:LIPIcs.SEA.2018.4,
  author =	{Henzinger, Alexandra and Noe, Alexander and Schulz, Christian},
  title =	{{ILP-based Local Search for Graph Partitioning}},
  booktitle =	{17th International Symposium on Experimental Algorithms (SEA 2018)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-070-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{103},
  editor =	{D'Angelo, Gianlorenzo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.4},
  URN =		{urn:nbn:de:0030-drops-89399},
  doi =		{10.4230/LIPIcs.SEA.2018.4},
  annote =	{Keywords: Graph Partitioning, Integer Linear Programming}
}
Document
DOI: 10.4230/LIPIcs.SEA.2017.4
Better Process Mapping and Sparse Quadratic Assignment

Authors: Christian Schulz and Jesper Larsson Träff

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)

Abstract
Communication and topology aware process mapping is a powerful approach to reduce communication time in parallel applications with known communication patterns on large, distributed memory systems. We address the problem as a quadratic assignment problem (QAP), and present algorithms to construct initial mappings of processes to processors as well as fast local search algorithms to further improve the mappings. By exploiting assumptions that typically hold for applications and modern supercomputer systems such as sparse communication patterns and hierarchically organized communication systems, we arrive at significantly more powerful algorithms for these special QAPs. Our multilevel construction algorithms employ recently developed, perfectly balanced graph partitioning techniques and excessively exploit the given communication system hierarchy. We present improvements to a local search algorithm of Brandfass et al. (2013), and decrease the running time by reducing the time needed to perform swaps in the assignment as well as by carefully constraining local search neighborhoods. Experiments indicate that our algorithms not only dramatically speed up local search, but due to the multilevel approach also find much better solutions in practice.
Cite as

Christian Schulz and Jesper Larsson Träff. Better Process Mapping and Sparse Quadratic Assignment. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{schulz_et_al:LIPIcs.SEA.2017.4,
  author =	{Schulz, Christian and Tr\"{a}ff, Jesper Larsson},
  title =	{{Better Process Mapping and Sparse Quadratic Assignment}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.4},
  URN =		{urn:nbn:de:0030-drops-76034},
  doi =		{10.4230/LIPIcs.SEA.2017.4},
  annote =	{Keywords: rank reordering, graph algorithms, process mapping, graph partitioning}
}
Document
DOI: 10.4230/LIPIcs.SEA.2017.30
Graph Partitioning with Acyclicity Constraints

Authors: Orlando Moreira, Merten Popp, and Christian Schulz

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)

Abstract
Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in multiprocessor scheduling. We identified the additional constraint of acyclic dependencies between blocks when mapping streaming applications to a heterogeneous embedded multiprocessor. Existing algorithms and heuristics do not address this requirement and deliver results that are not applicable for our use-case. In this work, we show that this more constrained version of the graph partitioning problem is NP-complete and present heuristics that achieve a close approximation of the optimal solution found by an exhaustive search for small problem instances and much better scalability for larger instances. In addition, we can show a positive impact on the schedule of a real imaging application that improves communication volume and execution time.
Cite as

Orlando Moreira, Merten Popp, and Christian Schulz. Graph Partitioning with Acyclicity Constraints. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{moreira_et_al:LIPIcs.SEA.2017.30,
  author =	{Moreira, Orlando and Popp, Merten and Schulz, Christian},
  title =	{{Graph Partitioning with Acyclicity Constraints}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.30},
  URN =		{urn:nbn:de:0030-drops-76042},
  doi =		{10.4230/LIPIcs.SEA.2017.30},
  annote =	{Keywords: Graph Partitioning, Computer Vision and Imaging Applications}
}
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