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Topology-induced Enhancement of Mappings [article]

Roland Glantz, Maria Predari, Henning Meyerhenke
2018 arXiv   pre-print
In this paper we propose a new method to enhance a mapping μ(·) of a parallel application's computational tasks to the processing elements (PEs) of a parallel computer. The idea behind our method is to enhance such a mapping by drawing on the observation that many topologies take the form of a partial cube. This class of graphs includes all rectangular and cubic meshes, any such torus with even extensions in each dimension, all hypercubes, and all trees. Following previous work, we represent
more » ... parallel application and the parallel computer by graphs G_a = (V_a, E_a) and G_p = (V_p, E_p). G_p being a partial cube allows us to label its vertices, the PEs, by bitvectors such that the cost of exchanging one unit of information between two vertices u_p and v_p of G_p amounts to the Hamming distance between the labels of u_p and v_p. By transferring these bitvectors from V_p to V_a via μ^-1(·) and extending them to be unique on V_a, we can enhance μ(·) by swapping labels of V_a in a new way. Pairs of swapped labels are local the PEs, but not G_a. Moreover, permutations of the bitvectors' entries give rise to a plethora of hierarchies on the PEs. Through these hierarchies we turn into a hierarchical method for improving μ(·) that is complementary to state-of-the-art methods for computing μ(·) in the first place. In our experiments we use to enhance mappings of complex networks onto rectangular meshes and tori with 256 and 512 nodes, as well as hypercubes with 256 nodes. It turns out that common quality measures of mappings derived from state-of-the-art algorithms can be improved considerably.
arXiv:1804.07131v1 fatcat:mj5gfgotivakdfz36bqhnc4v6e

Shared Memory Parallel Subgraph Enumeration [article]

Raphael Kimmig and Henning Meyerhenke and Darren Strash
2017 arXiv   pre-print
The subgraph enumeration problem asks us to find all subgraphs of a target graph that are isomorphic to a given pattern graph. Determining whether even one such isomorphic subgraph exists is NP-complete---and therefore finding all such subgraphs (if they exist) is a time-consuming task. Subgraph enumeration has applications in many fields, including biochemistry and social networks, and interestingly the fastest algorithms for solving the problem for biochemical inputs are sequential. Since
more » ... depend on depth-first tree traversal, an efficient parallelization is far from trivial. Nevertheless, since important applications produce data sets with increasing difficulty, parallelism seems beneficial. We thus present here a shared-memory parallelization of the state-of-the-art subgraph enumeration algorithms RI and RI-DS (a variant of RI for dense graphs) by Bonnici et al. [BMC Bioinformatics, 2013]. Our strategy uses work stealing and our implementation demonstrates a significant speedup on real-world biochemical data---despite a highly irregular data access pattern. We also improve RI-DS by pruning the search space better; this further improves the empirical running times compared to the already highly tuned RI-DS.
arXiv:1705.09358v1 fatcat:pfhec2akffg5pgr63xocr2qjna

Approximating Betweenness Centrality in Fully-dynamic Networks [article]

Elisabetta Bergamini, Henning Meyerhenke
2015 arXiv   pre-print
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in networks that change over time. In this paper we propose the first betweenness centrality approximation algorithms with a provable
more » ... uarantee on the maximum approximation error for dynamic networks. Several new intermediate algorithmic results contribute to the respective approximation algorithms: (i) new upper bounds on the vertex diameter, (ii) the first fully-dynamic algorithm for updating an approximation of the vertex diameter in undirected graphs, and (iii) an algorithm with lower time complexity for updating single-source shortest paths in unweighted graphs after a batch of edge actions. Using approximation, our algorithms are the first to make in-memory computation of betweenness in dynamic networks with millions of edges feasible. Our experiments show that our algorithms can achieve substantial speedups compared to recomputation, up to several orders of magnitude. Moreover, the approximation accuracy is usually significantly better than the theoretical guarantee in terms of absolute error. More importantly, for reasonably small approximation error thresholds, the rank of nodes is well preserved, in particular for nodes with high betweenness.
arXiv:1510.07971v1 fatcat:hwohlqkl75htvm2kzsq4fa4wce

n-Level Hypergraph Partitioning [article]

Vitali Henne, Henning Meyerhenke, Peter Sanders, Sebastian Schlag, Christian Schulz
2015 arXiv   pre-print
We develop a multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time and thus allows very high quality. This includes a rating function that avoids nonuniform vertex weights, an efficient "semi-dynamic" hypergraph data structure, a very fast coarsening algorithm, and two new local search algorithms. One is a k-way hypergraph adaptation of Fiduccia-Mattheyses local search and gives high quality at reasonable cost. The other is an adaptation of size-constrained
more » ... abel propagation to hypergraphs. Comparisons with hMetis and PaToH indicate that the new algorithm yields better quality over several benchmark sets and has a running time that is comparable to hMetis. Using label propagation local search is several times faster than hMetis and gives better quality than PaToH for a VLSI benchmark set.
arXiv:1505.00693v1 fatcat:fbnwlpvj5vgqvff2s4rrweb4hu

Balanced k-means for Parallel Geometric Partitioning [article]

Moritz von Looz, Charilaos Tzovas, Henning Meyerhenke
2018 arXiv   pre-print
Mesh partitioning is an indispensable tool for efficient parallel numerical simulations. Its goal is to minimize communication between the processes of a simulation while achieving load balance. Established graph-based partitioning tools yield a high solution quality; however, their scalability is limited. Geometric approaches usually scale better, but their solution quality may be unsatisfactory for 'non-trivial' mesh topologies. In this paper, we present a scalable version of k-means that is
more » ... dapted to yield balanced clusters. Balanced k-means constitutes the core of our new partitioning algorithm Geographer. Bootstrapping of initial centers is performed with space-filling curves, leading to fast convergence of the subsequent balanced k-means algorithm. Our experiments with up to 16384 MPI processes on numerous benchmark meshes show the following: (i) Geographer produces partitions with a lower communication volume than state-of-the-art geometric partitioners from the Zoltan package; (ii) Geographer scales well on large inputs; (iii) a Delaunay mesh with a few billion vertices and edges can be partitioned in a few seconds.
arXiv:1805.01208v1 fatcat:d33hxupu5rgp7jj2mxdndfktu4

Updating Dynamic Random Hyperbolic Graphs in Sublinear Time [article]

Moritz von Looz, Henning Meyerhenke
2018 arXiv   pre-print
Meyerhenke, Institute of Computer Science, University of Cologne, Weyertal 121, 50931 Cologne, Germany; emails: mloozcor@uni-koeln.de, h.meyerhenke@uni-koeln.de.  ... 
arXiv:1802.03297v1 fatcat:cn7imz4awjhvvbyxo5rjnmegs4

Parallel Adaptive Sampling with almost no Synchronization [article]

Alexander van der Grinten, Eugenio Angriman, Henning Meyerhenke
2019 arXiv   pre-print
Approximation via sampling is a widespread technique whenever exact solutions are too expensive. In this paper, we present techniques for an efficient parallelization of adaptive (a. k. a. progressive) sampling algorithms on multi-threaded shared-memory machines. Our basic algorithmic technique requires no synchronization except for atomic load-acquire and store-release operations. It does, however, require O(n) memory per thread, where n is the size of the sampling state. We present variants
more » ... the algorithm that either reduce this memory consumption to O(1) or ensure that deterministic results are obtained. Using the KADABRA algorithm for betweenness centrality (a popular measure in network analysis) approximation as a case study, we demonstrate the empirical performance of our techniques. In particular, on a 32-core machine, our best algorithm is 2.9x faster than what we could achieve using a straightforward OpenMP-based parallelization and 65.3x faster than the existing implementation of KADABRA.
arXiv:1903.09422v1 fatcat:j54idjmu7ba3npbfwam7tdxon4

Maxent-Stress Optimization of 3D Biomolecular Models [article]

Michael Wegner, Oskar Taubert, Alexander Schug, Henning Meyerhenke
2017 arXiv   pre-print
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
more » ... 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.
arXiv:1706.06805v1 fatcat:d2ge522vqbdb3epfwyn4odtfdq

Faster Betweenness Centrality Updates in Evolving Networks [article]

Elisabetta Bergamini, Henning Meyerhenke, Mark Ortmann, Arie Slobbe
2017 arXiv   pre-print
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,
more » ... c). 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.
arXiv:1704.08592v1 fatcat:kuz2fdd3vjby5h6tukiegurn7e

Fully-dynamic Weighted Matching Approximation in Practice [article]

Eugenio Angriman, Henning Meyerhenke, Christian Schulz, Bora Uçar
2021 arXiv   pre-print
Meyerhenke, P. Sanders, C. Schulz, and D. Wagner. Benchmarking for Graph Clustering and Partitioning. In Encyclopedia of Social Network Analysis and Mining.  ... 
arXiv:2104.13098v1 fatcat:ol6w2tf2o5g3vdm4ul7z6i6fd4

Scaling up Group Closeness Maximization [article]

Elisabetta Bergamini, Tanya Gonser, Henning Meyerhenke
2019 arXiv   pre-print
Closeness is a widely-used centrality measure in social network analysis. For a node it indicates the reciprocal of the average shortest-path distance to the other nodes of the network. While the identification of the k nodes with highest closeness received significant attention, many applications are actually interested in finding a group of nodes that is central as a whole. For this problem, only recently a greedy algorithm has been proposed [Chen et al., ADC 2016]. The approximation factor
more » ... (1 - 1/e) proposed by Chen et al. for this algorithm does not hold, though, as we show in this version of our paper. Since their implementation of the greedy algorithm was still too slow for large networks, Chen et al. also proposed a heuristic without approximation guarantee. In the present paper we develop new techniques to speed up the greedy algorithm. Compared to the previous implementation, our approach is orders of magnitude faster and, compared to the heuristic proposed by Chen et al., we always find a solution with better quality in a comparable running time in our experiments. Our method Greedy++ allows us to estimate the group with maximum closeness on networks with up to hundreds of millions of edges in minutes or at most a few hours. The greedy approach by [Chen et al., ADC 2016] would take several days already on networks with hundreds of thousands of edges. Our experiments show that the solution found by Greedy++ is actually very close to the optimum (...) Note: This paper version fixes the issue of relying on the presumed (but incorrect) submodularity of group closeness. While this has implications on the theoretical assessment of the greedy algorithm, our algorithm variant and its implementation remain unaffected. The reason is that Greedy++ relies (among others) on the supermodularity of farness, which does hold.
arXiv:1710.01144v2 fatcat:hcwr6pedo5gaziadfyfgqt3ssu

Structure-Preserving Sparsification of Social Networks [article]

Gerd Lindner, Christian L. Staudt, Michael Hamann, Henning Meyerhenke, Dorothea Wagner
2015 arXiv   pre-print
Sparsification reduces the size of networks while preserving structural and statistical properties of interest. Various sparsifying algorithms have been proposed in different contexts. We contribute the first systematic conceptual and experimental comparison of edge sparsification methods on a diverse set of network properties. It is shown that they can be understood as methods for rating edges by importance and then filtering globally by these scores. In addition, we propose a new
more » ... n method (Local Degree) which preserves edges leading to local hub nodes. All methods are evaluated on a set of 100 Facebook social networks with respect to network properties including diameter, connected components, community structure, and multiple node centrality measures. Experiments with our implementations of the sparsification methods (using the open-source network analysis tool suite NetworKit) show that many network properties can be preserved down to about 20% of the original set of edges. Furthermore, the experimental results allow us to differentiate the behavior of different methods and show which method is suitable with respect to which property. Our Local Degree method is fast enough for large-scale networks and performs well across a wider range of properties than previously proposed methods.
arXiv:1505.00564v1 fatcat:gbjjb6axjreereppmbtkfylluy

Approximating Betweenness Centrality in Large Evolving Networks [article]

Elisabetta Bergamini and Henning Meyerhenke and Christian L. Staudt
2014 arXiv   pre-print
Betweenness centrality ranks the importance of nodes by their participation in all shortest paths of the network. Therefore computing exact betweenness values is impractical in large networks. For static networks, approximation based on randomly sampled paths has been shown to be significantly faster in practice. However, for dynamic networks, no approximation algorithm for betweenness centrality is known that improves on static recomputation. We address this deficit by proposing two
more » ... approximation algorithms (for weighted and unweighted connected graphs) which provide a provable guarantee on the absolute approximation error. Processing batches of edge insertions, our algorithms yield significant speedups up to a factor of 10^4 compared to restarting the approximation. This is enabled by investing memory to store and efficiently update shortest paths. As a building block, we also propose an asymptotically faster algorithm for updating the SSSP problem in unweighted graphs. Our experimental study shows that our algorithms are the first to make in-memory computation of a betweenness ranking practical for million-edge semi-dynamic networks. Moreover, our results show that the accuracy is even better than the theoretical guarantees in terms of absolutes errors and the rank of nodes is well preserved, in particular for those with high betweenness.
arXiv:1409.6241v1 fatcat:upgmws5h5zf3tpi677ruik76ay

Fully-dynamic Approximation of Betweenness Centrality [article]

Elisabetta Bergamini, Henning Meyerhenke
2015 arXiv   pre-print
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in evolving networks. In previous work we proposed the first semi-dynamic algorithms that recompute an approximation of betweenness in
more » ... connected graphs after batches of edge insertions. In this paper we propose the first fully-dynamic approximation algorithms (for weighted and unweighted undirected graphs that need not to be connected) with a provable guarantee on the maximum approximation error. The transfer to fully-dynamic and disconnected graphs implies additional algorithmic problems that could be of independent interest. In particular, we propose a new upper bound on the vertex diameter for weighted undirected graphs. For both weighted and unweighted graphs, we also propose the first fully-dynamic algorithms that keep track of such upper bound. In addition, we extend our former algorithm for semi-dynamic BFS to batches of both edge insertions and deletions. Using approximation, our algorithms are the first to make in-memory computation of betweenness in fully-dynamic networks with millions of edges feasible. Our experiments show that they can achieve substantial speedups compared to recomputation, up to several orders of magnitude.
arXiv:1504.07091v2 fatcat:zhe7ockhavbn7kywum725wzf2y

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
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