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Fully-dynamic Weighted Matching Approximation in Practice [article]

Eugenio Angriman, Henning Meyerhenke, Christian Schulz, Bora Uçar
2021 arXiv   pre-print
Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is based on random walks/paths combined with dynamic programming. The second algorithm has been introduced by Stubbs and Williams without an implementation. Roughly speaking, their algorithm uses dynamic unweighted matching algorithms as a subroutine (within a
more » ... ltilevel approach); this allows us to use previous work on dynamic unweighted matching algorithms as a black box in order to obtain a fully-dynamic weighted matching algorithm. We empirically study the algorithms on an extensive set of dynamic instances and compare them with optimal weighted matchings. Our experiments show that the random walk algorithm typically fares much better than Stubbs/Williams (regarding the time/quality tradeoff), and its results are often not far from the optimum.
arXiv:2104.13098v1 fatcat:ol6w2tf2o5g3vdm4ul7z6i6fd4

Parallel Adaptive Sampling with almost no Synchronization [article]

Alexander van der Grinten, Eugenio Angriman, Henning Meyerhenke
2019 arXiv   pre-print
In the meantime, our code is available at https://gist.github.com/angriman/ cfb729c1c369198b8a1a36aad1f52fcc.  ... 
arXiv:1903.09422v1 fatcat:j54idjmu7ba3npbfwam7tdxon4

Local Search for Group Closeness Maximization on Big Graphs [article]

Eugenio Angriman, Alexander van der Grinten, Henning Meyerhenke
2019 arXiv   pre-print
In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group closeness maximization, in turn, is more challenging: the objective is to find a vertex group that is central as a whole and state-of-the-art heuristics for it do not scale to very big graphs yet. In this paper, we present new local search heuristics for group
more » ... eness maximization. By using randomized approximation techniques and dynamic data structures, our algorithms are often able to perform locally optimal decisions efficiently. The final result is a group with high (but not optimal) closeness centrality. We compare our algorithms to the current state-of-the-art greedy heuristic both on weighted and on unweighted real-world graphs. For graphs with hundreds of millions of edges, our local search algorithms take only around ten minutes, while greedy requires more than ten hours. Overall, our new algorithms are between one and two orders of magnitude faster, depending on the desired group size and solution quality. For example, on weighted graphs and k = 10, our algorithms yield solutions of 12,4% higher quality, while also being 793,6× faster. For unweighted graphs and k = 10, we achieve solutions within 99,4% of the state-of-the-art quality while being 127,8× faster.
arXiv:1911.03360v1 fatcat:cqerj377nngfpd6g6wm43y7vcq

Group Centrality Maximization for Large-scale Graphs [article]

Eugenio Angriman, Alexander van der Grinten, Aleksandar Bojchevski, Daniel Zügner, Stephan Günnemann, Henning Meyerhenke
2019 arXiv   pre-print
The study of vertex centrality measures is a key aspect of network analysis. Naturally, such centrality measures have been generalized to groups of vertices; for popular measures it was shown that the problem of finding the most central group is NP-hard. As a result, approximation algorithms to maximize group centralities were introduced recently. Despite a nearly-linear running time, approximation algorithms for group betweenness and (to a lesser extent) group closeness are rather slow on
more » ... networks due to high constant overheads. That is why we introduce GED-Walk centrality, a new submodular group centrality measure inspired by Katz centrality. In contrast to closeness and betweenness, it considers walks of any length rather than shortest paths, with shorter walks having a higher contribution. We define algorithms that (i) efficiently approximate the GED-Walk score of a given group and (ii) efficiently approximate the (proved to be NP-hard) problem of finding a group with highest GED-Walk score. Experiments on several real-world datasets show that scores obtained by GED-Walk improve performance on common graph mining tasks such as collective classification and graph-level classification. An evaluation of empirical running times demonstrates that maximizing GED-Walk (in approximation) is two orders of magnitude faster compared to group betweenness approximation and for group sizes ≤ 100 one to two orders faster than group closeness approximation. For graphs with tens of millions of edges, approximate GED-Walk maximization typically needs less than one minute. Furthermore, our experiments suggest that the maximization algorithms scale linearly with the size of the input graph and the size of the group.
arXiv:1910.13874v1 fatcat:2yfx6ozwybfb7hc7gl24j4sse4

Guidelines for Experimental Algorithmics in Network Analysis [article]

Eugenio Angriman, Alexander van der Grinten, Moritz von Looz, Henning Meyerhenke, Martin Nöllenburg, Maria Predari, Charilaos Tzovas
2019 arXiv   pre-print
The field of network science is a highly interdisciplinary area; for the empirical analysis of network data, it draws algorithmic methodologies from several research fields. Hence, research procedures and descriptions of the technical results often differ, sometimes widely. In this paper we focus on methodologies for the experimental part of algorithm engineering for network analysis -- an important ingredient for a research area with empirical focus. More precisely, we unify and adapt existing
more » ... recommendations from different fields and propose universal guidelines -- including statistical analyses -- for the systematic evaluation of network analysis algorithms. This way, the behavior of newly proposed algorithms can be properly assessed and comparisons to existing solutions become meaningful. Moreover, as the main technical contribution, we provide SimexPal, a highly automated tool to perform and analyze experiments following our guidelines. To illustrate the merits of SimexPal and our guidelines, we apply them in a case study: we design, perform, visualize and evaluate experiments of a recent algorithm for approximating betweenness centrality, an important problem in network analysis. In summary, both our guidelines and SimexPal shall modernize and complement previous efforts in experimental algorithmics; they are not only useful for network analysis, but also in related contexts.
arXiv:1904.04690v1 fatcat:ezht55uuvvg4phth4n3cx7htna

New Approximation Algorithms for Forest Closeness Centrality – for Individual Vertices and Vertex Groups [article]

Alexander van der Grinten, Eugenio Angriman, Maria Predari, Henning Meyerhenke
2021 arXiv   pre-print
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest closeness centrality; it is closely related to electrical measures using current flow but can also handle disconnected graphs. Recently, [Jin et al., ICDM'19] proposed an algorithm to approximate this measure probabilistically. Their algorithm processes small inputs
more » ... uickly, but does not scale well beyond hundreds of thousands of vertices. In this paper, we first propose a different approximation algorithm; it is up to two orders of magnitude faster and more accurate in practice. Our method exploits the strong connection between uniform spanning trees and forest distances by adapting and extending recent approximation algorithms for related single-vertex problems. This results in a nearly-linear time algorithm with an absolute probabilistic error guarantee. In addition, we are the first to consider the problem of finding an optimal group of vertices w.r.t. forest closeness. We prove that this latter problem is NP-hard; to approximate it, we adapt a greedy algorithm by [Li et al., WWW'19], which is based on (partial) matrix inversion. Moreover, our experiments show that on disconnected graphs, group forest closeness outperforms existing centrality measures in the context of semi-supervised vertex classification.
arXiv:2101.06192v1 fatcat:v7ks2xvembdcxhr735xehmpbde

Guidelines for Experimental Algorithmics: A Case Study in Network Analysis

Eugenio Angriman, Alexander van der Grinten, Moritz von Looz, Henning Meyerhenke, Martin Nöllenburg, Maria Predari, Charilaos Tzovas
2019 Algorithms  
The field of network science is a highly interdisciplinary area; for the empirical analysis of network data, it draws algorithmic methodologies from several research fields. Hence, research procedures and descriptions of the technical results often differ, sometimes widely. In this paper we focus on methodologies for the experimental part of algorithm engineering for network analysis—an important ingredient for a research area with empirical focus. More precisely, we unify and adapt existing
more » ... ommendations from different fields and propose universal guidelines—including statistical analyses—for the systematic evaluation of network analysis algorithms. This way, the behavior of newly proposed algorithms can be properly assessed and comparisons to existing solutions become meaningful. Moreover, as the main technical contribution, we provide , a highly automated tool to perform and analyze experiments following our guidelines. To illustrate the merits of and our guidelines, we apply them in a case study: we design, perform, visualize and evaluate experiments of a recent algorithm for approximating betweenness centrality, an important problem in network analysis. In summary, both our guidelines and shall modernize and complement previous efforts in experimental algorithmics; they are not only useful for network analysis, but also in related contexts.
doi:10.3390/a12070127 fatcat:ulqlmghp4remzotmjwggdkdxmu

Computing Top-k Closeness Centrality in Fully-dynamic Graphs [chapter]

Patrick Bisenius, Elisabetta Bergamin, Eugenio Angriman, Henning Meyerhenke
2018 2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)  
Closeness is a widely-studied centrality measure. Since it requires all pairwise distances, computing closeness for all nodes is infeasible for large real-world networks. However, for many applications, it is only necessary to find the k most central nodes and not all closeness values. Prior work has shown that computing the top-k nodes with highest closeness can be done much faster than computing closeness for all nodes in real-world networks. However, for networks that evolve over time, no
more » ... amic top-k closeness algorithm exists that improves on static recomputation. In this paper, we present several techniques that allow us to efficiently compute the k nodes with highest (harmonic) closeness after an edge insertion or an edge deletion. Our algorithms use information obtained during earlier computations to omit unnecessary work. However, they do not require asymptotically more memory than the static algorithms (i. e., linear in the number of nodes). We propose separate algorithms for complex networks (which exhibit the small-world property) and networks with large diameter such as street networks, and we compare them against static recomputation on a variety of real-world networks. On many instances, our dynamic algorithms are two orders of magnitude faster than recomputation; on some large graphs, we even reach average speedups between 10 3 and 10 4 .
doi:10.1137/1.9781611975055.3 dblp:conf/alenex/BiseniusBAM18 fatcat:hf6wjs7uhzdebg6nrv7zdellvy

Approximation of the Diagonal of a Laplacian's Pseudoinverse for Complex Network Analysis [article]

Eugenio Angriman, Maria Predari, Alexander van der Grinten, Henning Meyerhenke
2021 arXiv   pre-print
Eugenio Angriman, Maria Predari, Alexander van der Grinten, and Henning Meyerhenke. Haim Avron and Sivan Toledo.  ...  Scientific Computing, 37(2):C268-C284, 2015. doi: 10.1137/120902616. 4 Approximation of the diagonal of a laplacian's pseudoinverse for complex network analysis, 2020. arXiv:2006.13679. 5 Eugenio Angriman  ... 
arXiv:2006.13679v2 fatcat:e6c57yt5nnepbitwrqljuozeqe

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

Eugenio Angriman, Maria Predari, Alexander van der Grinten, Henning Meyerhenke, Peter Sanders, Fabrizio Grandoni, Grzegorz Herman
2020 European Symposium on Algorithms  
Angriman, M. Predari, A. van der Grinten, and H.  ... 
doi:10.4230/lipics.esa.2020.6 dblp:conf/esa/AngrimanPGM20 fatcat:ucyir4c7bbaala4zhfsxp6ocmq

Guidelines for Experimental Algorithmics: A Case Study in Network Analysis

Eugenio Angriman, Alexander Van Der Grinten, Moritz Von Looz, Henning Meyerhenke, Martin Nöllenburg, Maria Predari, Charilaos Tzovas, Humboldt-Universität Zu Berlin, Humboldt-Universität Zu Berlin
2019
The field of network science is a highly interdisciplinary area; for the empirical analysis of network data, it draws algorithmic methodologies from several research fields. Hence, research procedures and descriptions of the technical results often differ, sometimes widely. In this paper we focus on methodologies for the experimental part of algorithm engineering for network analysis—an important ingredient for a research area with empirical focus. More precisely, we unify and adapt existing
more » ... ommendations from different fields and propose universal guidelines—including statistical analyses—for the systematic evaluation of network analysis algorithms. This way, the behavior of newly proposed algorithms can be properly assessed and comparisons to existing solutions become meaningful. Moreover, as the main technical contribution, we provide SimexPal, a highly automated tool to perform and analyze experiments following our guidelines. To illustrate the merits of SimexPal and our guidelines, we apply them in a case study: we design, perform, visualize and evaluate experiments of a recent algorithm for approximating betweenness centrality, an important problem in network analysis. In summary, both our guidelines and SimexPal shall modernize and complement previous efforts in experimental algorithmics; they are not only useful for network analysis, but also in related contexts.
doi:10.18452/20500 fatcat:hhczjslqpna73j63e44isib4ta

Algorithms for Big Data

Ulrich Meyer, Ziawasch Abedjan
2020 it - Information Technology  
-The article "Scaling up network centrality computations -A brief overview" by Alexander van der Grinten, Eugenio Angriman, and Henning Meyerhenke (Humboldt University Berlin) reviews several common and  ... 
doi:10.1515/itit-2020-0008 fatcat:v6seqg4ksjatlcagmzyercbv7u

Exposición de Eugenio Raúl Zaffaroni ante el Tribunal Supremo del Estado Plurinacional de Bolivia

Revista Derechos en Acción
2020 Derechos en Acción  
Exposición de Eugenio Raúl Zaffaroni ante el Tribunal Supremo del Estado Plurinacional de Bolivia.  ...  Graciela Angriman nos ha ilustrado al respecto en "Derechos de las mujeres, género y prisión" (2017) respecto del "uso del sistema penal para controlar y modelar a la mujer, bajo representaciones y roles  ... 
doi:10.24215/25251678e450 fatcat:tteg64slvfh2tlezzhutbbnpnm

Scaling up Group Closeness Maximization [article]

Elisabetta Bergamini, Tanya Gonser, Henning Meyerhenke
2019 arXiv   pre-print
Acknowledgments We are very grateful to Eugenio Angriman and Alexander van der Grinten (both HU Berlin) for providing the counterexample we presented in Section 3.2 regarding the submodularity of group  ... 
arXiv:1710.01144v2 fatcat:hcwr6pedo5gaziadfyfgqt3ssu

Algorithms for the Identification of Central Nodes in Large Real-World Networks

Elisabetta Bergamini
2018
The results presented in Chapter 10 are joint work with Patrick Bisenius, Eugenio Angriman and Henning Meyerhenke and have been accepted for publication at the Twentieth Workshop on Algorithm Engineering  ...  Angriman and Henning Meyerhenke and have been accepted for publication at the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX 2018).  ... 
doi:10.5445/ir/1000085647 fatcat:bvl7ephnyfhh5blupsfgddn2aq
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