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Documents authored by Meyerhenke, Henning


Document
Approximation of the Diagonal of a Laplacian’s Pseudoinverse for Complex Network Analysis

Authors: Eugenio Angriman, Maria Predari, Alexander van der Grinten, and Henning Meyerhenke

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


Abstract
The ubiquity of massive graph data sets in numerous applications requires fast algorithms for extracting knowledge from these data. We are motivated here by three electrical measures for the analysis of large small-world graphs G = (V, E) - i. e., graphs with diameter in O(log |V|), which are abundant in complex network analysis. From a computational point of view, the three measures have in common that their crucial component is the diagonal of the graph Laplacian’s pseudoinverse, L^+. Computing diag(L^+) exactly by pseudoinversion, however, is as expensive as dense matrix multiplication - and the standard tools in practice even require cubic time. Moreover, the pseudoinverse requires quadratic space - hardly feasible for large graphs. Resorting to approximation by, e. g., using the Johnson-Lindenstrauss transform, requires the solution of O(log |V| / ε²) Laplacian linear systems to guarantee a relative error, which is still very expensive for large inputs. In this paper, we present a novel approximation algorithm that requires the solution of only one Laplacian linear system. The remaining parts are purely combinatorial - mainly sampling uniform spanning trees, which we relate to diag(L^+) via effective resistances. For small-world networks, our algorithm obtains a ± ε-approximation with high probability, in a time that is nearly-linear in |E| and quadratic in 1 / ε. Another positive aspect of our algorithm is its parallel nature due to independent sampling. We thus provide two parallel implementations of our algorithm: one using OpenMP, one MPI + OpenMP. In our experiments against the state of the art, our algorithm (i) yields more accurate approximation results for diag(L^+), (ii) is much faster and more memory-efficient, and (iii) obtains good parallel speedups, in particular in the distributed setting.

Cite as

Eugenio Angriman, Maria Predari, Alexander van der Grinten, and Henning Meyerhenke. Approximation of the Diagonal of a Laplacian’s Pseudoinverse for Complex Network Analysis. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 6:1-6:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{angriman_et_al:LIPIcs.ESA.2020.6,
  author =	{Angriman, Eugenio and Predari, Maria and van der Grinten, Alexander and Meyerhenke, Henning},
  title =	{{Approximation of the Diagonal of a Laplacian’s Pseudoinverse for Complex Network Analysis}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{6:1--6:24},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.6},
  URN =		{urn:nbn:de:0030-drops-128723},
  doi =		{10.4230/LIPIcs.ESA.2020.6},
  annote =	{Keywords: Laplacian pseudoinverse, electrical centrality measures, uniform spanning tree, effective resistance, parallel sampling}
}
Document
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-dev.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
High-Performance Graph Algorithms (Dagstuhl Seminar 18241)

Authors: Henning Meyerhenke, Richard Peng, and Ilya Safro

Published in: Dagstuhl Reports, Volume 8, Issue 6 (2019)


Abstract
This report documents the program and outcomes of Dagstuhl Seminar 18241 ``High-performance Graph Algorithms''. The seminar reflected the ongoing qualitative change how graph algorithms are used in practice due to (i) the complex structure of graphs in new and emerging applications, (ii) the size of typical inputs, and (iii) the computer systems with which graph problems are solved. This change is having a tremendous impact on the field of graph algorithms in terms of algorithm theory and implementation as well as hardware requirements and application areas. The seminar covered recent advances in all these aspects, trying to balance and mediate between theory and practice. The abstracts included in this report contain and survey recent state-of-the-art results, but also point to promising new directions for high-performance graph algorithms and their applications, both from a theoretical and a practical point of view.

Cite as

Henning Meyerhenke, Richard Peng, and Ilya Safro. High-Performance Graph Algorithms (Dagstuhl Seminar 18241). In Dagstuhl Reports, Volume 8, Issue 6, pp. 19-39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@Article{meyerhenke_et_al:DagRep.8.6.19,
  author =	{Meyerhenke, Henning and Peng, Richard and Safro, Ilya},
  title =	{{High-Performance Graph Algorithms (Dagstuhl Seminar 18241)}},
  pages =	{19--39},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2018},
  volume =	{8},
  number =	{6},
  editor =	{Meyerhenke, Henning and Peng, Richard and Safro, Ilya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.8.6.19},
  URN =		{urn:nbn:de:0030-drops-100475},
  doi =		{10.4230/DagRep.8.6.19},
  annote =	{Keywords: algorithm engineering, combinatorial scientific computing, graph algorithms, high-performance computing, theoretical computer science}
}
Document
Scalable Katz Ranking Computation in Large Static and Dynamic Graphs

Authors: Alexander van der Grinten, Elisabetta Bergamini, Oded Green, David A. Bader, and Henning Meyerhenke

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)


Abstract
Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz centrality is one of the established centrality measures. In this paper, we consider the problem of computing rankings for Katz centrality. In particular, we propose upper and lower bounds on the Katz score of a given node. While previous approaches relied on numerical approximation or heuristics to compute Katz centrality rankings, we construct an algorithm that iteratively improves those upper and lower bounds until a correct Katz ranking is obtained. We extend our algorithm to dynamic graphs while maintaining its correctness guarantees. Experiments demonstrate that our static graph algorithm outperforms both numerical approaches and heuristics with speedups between 1.5 x and 3.5 x, depending on the desired quality guarantees. Our dynamic graph algorithm improves upon the static algorithm for update batches of less than 10000 edges. We provide efficient parallel CPU and GPU implementations of our algorithms that enable near real-time Katz centrality computation for graphs with hundreds of millions of nodes in fractions of seconds.

Cite as

Alexander van der Grinten, Elisabetta Bergamini, Oded Green, David A. Bader, and Henning Meyerhenke. Scalable Katz Ranking Computation in Large Static and Dynamic Graphs. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{vandergrinten_et_al:LIPIcs.ESA.2018.42,
  author =	{van der Grinten, Alexander and Bergamini, Elisabetta and Green, Oded and Bader, David A. and Meyerhenke, Henning},
  title =	{{Scalable Katz Ranking Computation in Large Static and Dynamic Graphs}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.42},
  URN =		{urn:nbn:de:0030-drops-95055},
  doi =		{10.4230/LIPIcs.ESA.2018.42},
  annote =	{Keywords: network analysis, Katz centrality, top-k ranking, dynamic graphs, parallel algorithms}
}
Document
Maxent-Stress Optimization of 3D Biomolecular Models

Authors: Michael Wegner, Oskar Taubert, Alexander Schug, and Henning Meyerhenke

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)


Abstract
Knowing a biomolecule's structure is inherently linked to and a prerequisite for any detailed understanding of its function. Significant effort has gone into developing technologies for structural characterization. These technologies do not directly provide 3D structures; instead they typically yield noisy and erroneous distance information between specific entities such as atoms or residues, which have to be translated into consistent 3D models. Here we present an approach for this translation process based on maxent-stress optimization. Our new approach extends the original graph drawing method for the new application's specifics by introducing additional constraints and confidence values as well as algorithmic components. Extensive experiments demonstrate that our approach infers structural models (i.e., sensible 3D coordinates for the molecule's atoms) that correspond well to the distance information, can handle noisy and error-prone data, and is considerably faster than established tools. Our results promise to allow domain scientists nearly-interactive structural modeling based on distance constraints.

Cite as

Michael Wegner, Oskar Taubert, Alexander Schug, and Henning Meyerhenke. Maxent-Stress Optimization of 3D Biomolecular Models. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 70:1-70:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{wegner_et_al:LIPIcs.ESA.2017.70,
  author =	{Wegner, Michael and Taubert, Oskar and Schug, Alexander and Meyerhenke, Henning},
  title =	{{Maxent-Stress Optimization of 3D Biomolecular Models}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{70:1--70:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.70},
  URN =		{urn:nbn:de:0030-drops-78175},
  doi =		{10.4230/LIPIcs.ESA.2017.70},
  annote =	{Keywords: Distance geometry, protein structure determination, 3D graph drawing, maxent-stress optimization}
}
Document
Faster Betweenness Centrality Updates in Evolving Networks

Authors: Elisabetta Bergamini, Henning Meyerhenke, Mark Ortmann, and Arie Slobbe

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


Abstract
Finding central nodes is a fundamental problem in network analysis. Betweenness centrality is a well-known measure which quantifies the importance of a node based on the fraction of shortest paths going though it. Due to the dynamic nature of many today’s networks, algorithms that quickly update centrality scores have become a necessity. For betweenness, several dynamic algorithms have been proposed over the years, targeting different update types (incremental- and decremental-only, fully-dynamic). In this paper we introduce a new dynamic algorithm for updating betweenness centrality after an edge insertion or an edge weight decrease. Our method is a combination of two independent contributions: a faster algorithm for updating pairwise distances as well as number of shortest paths, and a faster algorithm for updating dependencies. Whereas the worst-case running time of our algorithm is the same as recomputation, our techniques considerably reduce the number of operations performed by existing dynamic betweenness algorithms. Our experimental evaluation on a variety of real-world networks reveals that our approach is significantly faster than the current state-of-the-art dynamic algorithms, approximately by one order of magnitude on average.

Cite as

Elisabetta Bergamini, Henning Meyerhenke, Mark Ortmann, and Arie Slobbe. Faster Betweenness Centrality Updates in Evolving Networks. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{bergamini_et_al:LIPIcs.SEA.2017.23,
  author =	{Bergamini, Elisabetta and Meyerhenke, Henning and Ortmann, Mark and Slobbe, Arie},
  title =	{{Faster Betweenness Centrality Updates in Evolving Networks}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{23:1--23:16},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.23},
  URN =		{urn:nbn:de:0030-drops-76093},
  doi =		{10.4230/LIPIcs.SEA.2017.23},
  annote =	{Keywords: Graph algorithms, shortest paths, distances, dynamic algorithms}
}
Document
High-performance Graph Algorithms and Applications in Computational Science (Dagstuhl Seminar 14461)

Authors: Ulrich Carsten Meyer, Henning Meyerhenke, Ali Pinar, and Ilya Safro

Published in: Dagstuhl Reports, Volume 4, Issue 11 (2015)


Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 14461 "High- performance Graph Algorithms and Applications in Computational Science". The seminar reflected the recent qualitative change how graph algorithms are used in practice due to (i) the complex structure of graphs in new and emerging applications, (ii) the size of typical inputs, and (iii) the computer systems on which graph problems are solved. This change is having a tremendous impact on the field of graph algorithms in terms of algorithm theory and implementation as well as hardware requirements and application areas. The seminar covered recent advances in all these aspects with a focus on practical algorithms and their efficient implementation for large-scale problems. The abstracts included in this report contain recent state-of-the-art results, but also point to promising new directions for high-performance graph algorithms and their applications.

Cite as

Ulrich Carsten Meyer, Henning Meyerhenke, Ali Pinar, and Ilya Safro. High-performance Graph Algorithms and Applications in Computational Science (Dagstuhl Seminar 14461). In Dagstuhl Reports, Volume 4, Issue 11, pp. 40-58, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@Article{meyer_et_al:DagRep.4.11.40,
  author =	{Meyer, Ulrich Carsten and Meyerhenke, Henning and Pinar, Ali and Safro, Ilya},
  title =	{{High-performance Graph Algorithms and Applications in Computational Science (Dagstuhl Seminar 14461)}},
  pages =	{40--58},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2015},
  volume =	{4},
  number =	{11},
  editor =	{Meyer, Ulrich Carsten and Meyerhenke, Henning and Pinar, Ali and Safro, Ilya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.4.11.40},
  URN =		{urn:nbn:de:0030-drops-49697},
  doi =		{10.4230/DagRep.4.11.40},
  annote =	{Keywords: graphs, graph algorithms, graph theory, computational science, complex networks, network science, graph partitioning, linear algebra, parallel program}
}
Document
On Dynamic Graph Partitioning and Graph Clustering using Diffusion

Authors: Henning Meyerhenke and Joachim Gehweiler

Published in: Dagstuhl Seminar Proceedings, Volume 10261, Algorithm Engineering (2010)


Abstract
Load balancing is an important requirement for the efficient execution of parallel numerical simulations. In particular when the simulation domain changes over time, the mapping of computational tasks to processors needs to be modified accordingly. State-of-the-art libraries for this problem are based on graph repartitioning. They have a number of drawbacks, including the optimized metric and the difficulty of parallelizing the popular repartitioning heuristic Kernighan-Lin (KL). Here we further explore the very promising diffusion-based graph partitioning algorithm DIBAP (Meyerhenke et al., JPDC 69(9):750–761, 2009) by adapting DIBAP to the related problem of load balancing. The presented experiments with graph sequences that imitate adaptive numerical simulations demonstrate the applicability and high quality of DIBAP for load balancing by repartitioning. Compared to the faster state-of-the-art repartitioners PARMETIS and parallel JOSTLE, DIBAP’s solutions have partitions with significantly fewer external edges and boundary nodes and the resulting average migration volume in the important maximum norm is also the best in most cases. We also prove that one of DIBAP's key components optimizes a relaxed version of the minimum edge cut problem. Moreover, we hint at a distributed algorithm based on ideas used in DIBAP for clustering a virtual P2P supercomputer.

Cite as

Henning Meyerhenke and Joachim Gehweiler. On Dynamic Graph Partitioning and Graph Clustering using Diffusion. In Algorithm Engineering. Dagstuhl Seminar Proceedings, Volume 10261, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{meyerhenke_et_al:DagSemProc.10261.4,
  author =	{Meyerhenke, Henning and Gehweiler, Joachim},
  title =	{{On Dynamic Graph Partitioning and Graph Clustering using Diffusion}},
  booktitle =	{Algorithm Engineering},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10261},
  editor =	{Giuseppe F. Italiano and David S. Johnson and Petra Mutzel and Peter Sanders},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10261.4},
  URN =		{urn:nbn:de:0030-drops-27980},
  doi =		{10.4230/DagSemProc.10261.4},
  annote =	{Keywords: Dynamic graph partitioning/clustering, disturbed diffusion, load balancing, relaxed cut optimization}
}
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