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29
Engineering Multilevel Graph Partitioning Algorithms
"... We present a multilevel graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from multigrid linear solvers. Local improvement algorithms are based on maxflow mincut computations and more localized FM searches. By combining these technique ..."
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Cited by 28 (14 self)
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We present a multilevel graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from multigrid linear solvers. Local improvement algorithms are based on maxflow mincut computations and more localized FM searches. By combining these techniques, we obtain an algorithm that is fast on the one hand and on the other hand is able to improve the best known partitioning results for many inputs. For example, in Walshaw’s well known benchmark tables we achieve 317 improvements for the tables at 1%, 3 % and 5 % imbalance. Moreover, in 118 out of the 295 remaining cases we have been able to reproduce the best cut in this benchmark.
Distributed Evolutionary Graph Partitioning
, 2012
"... We present a novel distributed evolutionary algorithm, KaFFPaE, to solve the Graph Partitioning Problem, which makes use of KaFFPa (Karlsruhe Fast Flow Partitioner). The use of our multilevel graph partitioner KaFFPa provides new effective crossover and mutation operators. By combining these with a ..."
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Cited by 25 (11 self)
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We present a novel distributed evolutionary algorithm, KaFFPaE, to solve the Graph Partitioning Problem, which makes use of KaFFPa (Karlsruhe Fast Flow Partitioner). The use of our multilevel graph partitioner KaFFPa provides new effective crossover and mutation operators. By combining these with a scalable communication protocol we obtain a system that is able to improve the best known partitioning results for many inputs in a very short amount of time. For example, in Walshaw’s well known benchmark tables we are able to improve or recompute 76 % of entries for the tables with 1%, 3 % and 5 % imbalance.
A Multilevel Memetic Approach for Improving Graph Kpartitions
, 2011
"... Graph partitioning is one of the most studied NPcomplete problems. Given a graph G = (V, E), the task is to partition the vertex set V into k disjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this work, we present a highly ef ..."
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Cited by 13 (5 self)
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Graph partitioning is one of the most studied NPcomplete problems. Given a graph G = (V, E), the task is to partition the vertex set V into k disjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this work, we present a highly effective multilevel memetic algorithm, which integrates a new multiparent crossover operator and a powerful perturbationbased tabu search algorithm. The proposed crossover operator tends to preserve the backbone with respect to a certain number of parent individuals, i.e. the grouping of vertices which is common to all parent individuals. Extensive experimental studies on numerous benchmark instances from the Graph Partitioning Archive show that the proposed approach, within a time limit ranging from several minutes to several hours, performs far better than any of the existing graph partitioning algorithm in terms of solution quality.
Think Locally, Act Globally: Highly Balanced Graph Partitioning
"... We present a novel local improvement scheme for graph partitions that allows to enforce strict balance constraints. Using negative cycle detection algorithms this scheme combines local searches that individually violate the balance constraint into a more global feasible improvement. We combine this ..."
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Cited by 11 (9 self)
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We present a novel local improvement scheme for graph partitions that allows to enforce strict balance constraints. Using negative cycle detection algorithms this scheme combines local searches that individually violate the balance constraint into a more global feasible improvement. We combine this technique with an algorithm to balance unbalanced solutions and integrate it into a parallel multilevel evolutionary algorithm, KaFFPaE, to tackle the problem. Overall, we obtain a system that is fast on the one hand and on the other hand is able to improve or reproduce many of the best known perfectly balanced partitioning results reported in the Walshaw benchmark.
Scalable multithreaded community detection in social networks
 in Workshop on Multithreaded Architectures and Applications (MTAAP
, 2012
"... Abstract—The volume of existing graphstructured data requires improved parallel tools and algorithms. Finding communities, smaller subgraphs densely connected within the subgraph than to the rest of the graph, plays a role both in developing new parallel algorithms as well as opening smaller portion ..."
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Cited by 9 (2 self)
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Abstract—The volume of existing graphstructured data requires improved parallel tools and algorithms. Finding communities, smaller subgraphs densely connected within the subgraph than to the rest of the graph, plays a role both in developing new parallel algorithms as well as opening smaller portions of the data to current analysis tools. We improve performance of our parallel community detection algorithm by 20 % on the massively multithreaded Cray XMT, evaluate its performance on the nextgeneration Cray XMT2, and extend its reach to Intelbased platforms with OpenMP. To our knowledge, not only is this the first massively parallel community detection algorithm but also the only such algorithm that achieves excellent performance and good parallel scalability across all these platforms. Our implementation analyzes a moderate sized graph with 105 million vertices and 3.3 billion edges in around 500 seconds on a four processor, 80logicalcore Intelbased system and 1100 seconds on a 64processor Cray XMT2.
Advanced Coarsening Schemes for Graph Partitioning
 IN PROCEEDINGS OF THE 11TH INTERNATIONAL SYMPOSIUM ON EXPERIMENTAL ALGORITHMS (SEA’12), SER. LNCS
, 2012
"... The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on largescale graphs. Most of the attention in designing the multi ..."
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Cited by 9 (7 self)
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The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on largescale graphs. Most of the attention in designing the multilevel partitioning frameworks has been on the refinement phase. In this work we focus on the coarsening phase, which is responsible for creating structurally similar to the original but smaller graphs. We compare different matching and AMGbased coarsening schemes, experiment with the algebraic distance between nodes, and demonstrate computational results on several classes of graphs that emphasize the running time and quality advantages of different coarsenings.
Scaling algorithms for approximate and exact maximum weight matching
, 2011
"... The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the ..."
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Cited by 9 (0 self)
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The maximum cardinality and maximum weight matching problems can be solved in time Õ(m √ n), a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article we demonstrate that this “m √ n barrier ” is extremely fragile, in the following sense. For any ɛ> 0, we give an algorithm that computes a (1 − ɛ)approximate maximum weight matching in O(mɛ −1 log ɛ −1) time, that is, optimal linear time for any fixed ɛ. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error. Our second contribution is a new exact maximum weight matching algorithm for integerweighted bipartite graphs that runs in time O(m √ n log N). This improves on the O(Nm √ n)time and O(m √ n log(nN))time algorithms known since the mid 1980s, for 1 ≪ log N ≪ log n. Here N is the maximum integer edge weight. 1
High quality graph partitioning
, 2013
"... We present an overview over our graph partitioners KaFFPa (Karlsruhe Fast Flow Partitioner) and KaFFPaE (KaFFPa Evolutionary). KaFFPa is a multilevel graph partitioning algorithm which on the one hand uses novel local improvement algorithms based on maxflow and mincut computations and more local ..."
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Cited by 7 (4 self)
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We present an overview over our graph partitioners KaFFPa (Karlsruhe Fast Flow Partitioner) and KaFFPaE (KaFFPa Evolutionary). KaFFPa is a multilevel graph partitioning algorithm which on the one hand uses novel local improvement algorithms based on maxflow and mincut computations and more localized FM searches and on the other hand uses more sophisticated global search strategies transferred from multigrid linear solvers. KaFFPaE is a distributed evolutionary algorithm to solve the Graph Partitioning Problem. KaFFPaE uses KaFFPa and provides new effective crossover and mutation operators. By combining these with a scalable communication protocol we obtain a system that is able to improve the best known partitioning results for many inputs.
Scalable and High Performance Betweenness Centrality on the GPU
 in Proceedings of the 26th ACM/IEEE International Conference on High Performance Computing, Networking, Storage, and Analysis (SC
, 2014
"... Abstract—Graphs that model social networks, numerical simulations, and the structure of the Internet are enormous and cannot be manually inspected. A popular metric used to analyze these networks is betweenness centrality, which has applications in community detection, power grid contingency analys ..."
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Cited by 6 (4 self)
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Abstract—Graphs that model social networks, numerical simulations, and the structure of the Internet are enormous and cannot be manually inspected. A popular metric used to analyze these networks is betweenness centrality, which has applications in community detection, power grid contingency analysis, and the study of the human brain. However, these analyses come with a high computational cost that prevents the examination of large graphs of interest. Prior GPU implementations suffer from large local data structures and inefficient graph traversals that limit scalability and performance. Here we present several hybrid GPU implementations, providing good performance on graphs of arbitrary structure rather than just scalefree graphs as was done previously. We achieve up to 13x speedup on highdiameter graphs and an average of 2.71x speedup overall over the best existing GPU algorithm. We observe near linear speedup and performance exceeding tens of GTEPS when running betweenness centrality on 192 GPUs. Keywords—GPUs, Graph Algorithms, Parallel Algorithms I.
Partitioning Complex Networks via Sizeconstrained Clustering
 in Proceedings of the 13th International Symposium on Experimental Algorithms (SEA’14), ser. LNCS
, 2014
"... Abstract. The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be part ..."
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Cited by 6 (5 self)
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Abstract. The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. In this paper, we describe a novel approach to partition graphs effectively especially if the networks have a highly irregular structure. More precisely, our algorithm provides graph coarsening by iteratively contracting sizeconstrained clusterings that are computed using a label propagation algorithm. The same algorithm that provides the sizeconstrained clusterings can also be used during uncoarsening as a fast and simple local search algorithm. Depending on the algorithm’s configuration, we are able to compute partitions of very high quality outperforming all competitors, or partitions that are comparable to the best competitor in terms of quality, hMetis, while being nearly an order of magnitude faster on average. The fastest configuration partitions the largest graph available to us with 3.3 billion edges using a single machine in about ten minutes while cutting less than half of the edges than the fastest competitor, kMetis. 1