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## Parallel Graph Partitioning for Complex Networks (2015)

Venue: | Proceedings of the 29th International Parallal and Distributed Processing Symposium |

Citations: | 1 - 1 self |

### Citations

4650 | The anatomy of a large-scale hypertextual web search engine
- Brin, Page
- 1998
(Show Context)
Citation Context ...s can handle this graph on our system. I. INTRODUCTION Graph partitioning (GP) is a key prerequisite for efficient large-scale parallel graph algorithms. A prominent example is the PageRank algorithm =-=[1]-=-, which is used by search engines such as Google to order web pages displayed to the user by their importance. As huge networks become abundant, there is a need for their parallel analysis. In many ca... |

1183 | V.: A fast and high quality multilevel scheme for partitioning irregular graphs
- Karypis, Kumar
- 1999
(Show Context)
Citation Context ...ctical methods are based on mostly graph theoretic aspects, in particular edge contraction and local search. There are many ways to create graph hierarchies such as matching-based schemes [12], [13], =-=[14]-=-, [15], [16] or variations thereof [17] and techniques similar to algebraic multigrid [18], [19], [20]. We refer the interested reader to the respective papers for more details. Well-known software pa... |

629 | Multilevel k-way Partitioning Scheme for Irregular Graphs
- Karypis, Kumar
- 1995
(Show Context)
Citation Context ...co and Party are no longer developed and have no parallel version, the others have been parallelized, too. Most probably the fastest available parallel code is the parallel version of Metis, ParMetis =-=[21]-=-. The parallel version of Jostle [13] applies local search to pairs of neighboring partitions and is restricted to the case where the number of blocks equals the number of processors. This paralleliza... |

534 | The University of Florida sparse matrix collection
- Davis, Hu
(Show Context)
Citation Context ...] youtube ≈1.1M ≈2.9M S [39] in-2004 ≈1.3M ≈13.6M S [36] packing ≈2.1M ≈17.4M M [36] enwiki ≈4.2M ≈91.9M S [41] channel ≈4.8M ≈42.6M M [36] hugebubble-10 ≈18.3M ≈27.5M M [36] nlpkkt240 ≈27.9M ≈373M M =-=[37]-=- uk-2002 ≈18.5M ≈262M S [41] del26 ≈67.1M ≈201M M [23] rgg26 ≈67.1M ≈575M M [23] Larger Web Graphs arabic-2005 ≈22.7M ≈553M S [41] sk-2005 ≈50.6M ≈1.8G S [41] uk-2007 ≈105.8M ≈3.3G S [41] Graph Famili... |

491 | Pregel: a system for large-scale graph processing
- Malewicz, Austern, et al.
- 2010
(Show Context)
Citation Context ...in their case. Due to the superiority of our new algorithm compared to ParMetis on large complex networks, further running time savings can be anticipated, also for related tools like Google’s Pregel =-=[43]-=-, Apache Giraph (https://giraph.apache.org/), Giraph++ [25], and GraphLab [44]. In future work we want to develop a very fast prepartitioner for such systems and we want to take advantage of the alrea... |

266 | The WebGraph Framework I: Compression Techniques
- Boldi, Vigna
- 2004
(Show Context)
Citation Context ...o point bandwidth between two nodes of more than 3700 MB/s. We use machine B for the scalability experiments in Section V-B. Instances: We evaluate our algorithms on graphs collected from [36], [37], =-=[38]-=-, [39]. Table I summarizes the main properties of the benchmark set. Our benchmark set includes a number of graphs from numeric simulations as well as social networks and web graphs. Moreover, we use ... |

183 |
Near linear time algorithm to detect community structures in large-scale networks
- Raghavan, Albert, et al.
- 2007
(Show Context)
Citation Context ...mes. However, significant imbalance is introduced by their method, so that their results are incomparable to ours. The label propagation clustering algorithm was initially proposed by Raghavan et al. =-=[26]-=-. Moreover, the label propagation algorithm has been used to partition networks by Uganer and Backstrom [27]. The authors do not use a multilevel scheme and rely on a given or random partition which a... |

140 | Distributed graphlab: A framework for machine learning in the cloud
- Low, Gonzalez, et al.
(Show Context)
Citation Context ...s on large complex networks, further running time savings can be anticipated, also for related tools like Google’s Pregel [43], Apache Giraph (https://giraph.apache.org/), Giraph++ [25], and GraphLab =-=[44]-=-. In future work we want to develop a very fast prepartitioner for such systems and we want to take advantage of the already computed partition in later multilevel iterations to further minimize the c... |

110 | Graph Partitioning Models for Parallel Computing.
- Hendrickson
- 2000
(Show Context)
Citation Context ...edges that run between blocks. It is well-known that there are more realistic (and more complicated) objective functions involving also the block that is worst and the number of its neighboring nodes =-=[2]-=-, but minimizing the cut size has been adopted as a kind of standard since it is usually highly correlated with the other formulations. The graph partitioning problem is NP-complete [3], [4] and there... |

96 |
Some simplified NP-complete problems
- Garey, Johnson, et al.
- 1974
(Show Context)
Citation Context ...ing nodes [2], but minimizing the cut size has been adopted as a kind of standard since it is usually highly correlated with the other formulations. The graph partitioning problem is NP-complete [3], =-=[4]-=- and there is no approximation algorithm with a constant ratio factor for general graphs [5]. Hence, heuristic algorithms are used in practice. A successful heuristic for partitioning large graphs is ... |

94 |
Finding good approximate vertex and edge partitions is np-hard
- Bui, Jones
- 1992
(Show Context)
Citation Context ...s usually highly correlated with the other formulations. The graph partitioning problem is NP-complete [3], [4] and there is no approximation algorithm with a constant ratio factor for general graphs =-=[5]-=-. Hence, heuristic algorithms are used in practice. A successful heuristic for partitioning large graphs is the multilevel graph partitioning (MGP) approach depicted in Figure 1, where the graph is re... |

90 | Graph Partitioning for High-Performance Scientific Simulations, in: - Schlogel, Karypis, et al. - 2000 |

81 | Mesh Partitioning: a Multilevel Balancing and Refinement Algorithm,
- Walshaw, Cross
- 2000
(Show Context)
Citation Context ...ing time compared to the results computed by ParMetis, so that we do not present detailed data for PT-Scotch. Our default value for the allowed imbalance is 3% since this is one of the values used in =-=[35]-=- and the default value in Metis. By default we perform ten repetitions for each configuration of the algorithm using different random seeds for initialization and report the arithmetic average of comp... |

68 | Gps: A graph processing system.
- Salihoglu, Widom
- 2012
(Show Context)
Citation Context ... scenario are large-scale graph processing toolkits based on cloud computing. Significant savings for several algorithmic kernels within the toolkit GPS have been reported by using graph partitioning =-=[42]-=- – ParMetis in their case. Due to the superiority of our new algorithm compared to ParMetis on large complex networks, further running time savings can be anticipated, also for related tools like Goog... |

61 | Multilevel algorithms for partitioning powerlaw graphs, in:
- Abou-Rjeili, Karypis
- 2006
(Show Context)
Citation Context ...h theoretic aspects, in particular edge contraction and local search. There are many ways to create graph hierarchies such as matching-based schemes [12], [13], [14], [15], [16] or variations thereof =-=[17]-=- and techniques similar to algebraic multigrid [18], [19], [20]. We refer the interested reader to the respective papers for more details. Well-known software packages based on this approach include C... |

60 | A combined evolutionary search and multilevel optimisation approach to graph partitioning.
- Soperm, Walshaw, et al.
- 2004
(Show Context)
Citation Context ...alled KaFFPa, as well as several coarse-grained parallel and sequential meta-heuristics. The algorithms in KaHIP have been able to improve the best known partitioning results in the Walshaw Benchmark =-=[32]-=- for many inputs using a short amount of time to create the partitions. Recently, also specialized methods to partition social networks and web graphs have been included into the framework [7]. In thi... |

57 | Multilevel Refinement for Combinatorial Optimisation Problems
- Walshaw
- 2001
(Show Context)
Citation Context ...d. However, one can do better by transferring the solution of the previous multilevel iteration down the hierarchy. In the graph partitioning context, the notion of V-cycles was introduced by Walshaw =-=[33]-=-. More recent work augmented them to more complex cycles [34]. These previous works use matching-based coarsening with cut edges not being matched (and hence cut edges are not contracted). Thus, a giv... |

36 | JOSTLE: Parallel Multilevel Graph-Partitioning Software – An Overview.
- Walshaw, Cross
- 2007
(Show Context)
Citation Context ...nt practical methods are based on mostly graph theoretic aspects, in particular edge contraction and local search. There are many ways to create graph hierarchies such as matching-based schemes [12], =-=[13]-=-, [14], [15], [16] or variations thereof [17] and techniques similar to algebraic multigrid [18], [19], [20]. We refer the interested reader to the respective papers for more details. Well-known softw... |

33 | Engineering a scalable high quality graph partitioner. In: IPDPS,
- Holtgrewe, Sanders, et al.
- 2010
(Show Context)
Citation Context ... performing several independent attempts in parallel. The involved communication effort is reduced by considering only nodes close to the boundary of the current partitioning (band-refinement). KaPPa =-=[23]-=- is a parallel matching-based MGP algorithm which is also restricted to the case where the number of blocks equals the number of processors used. PDiBaP [24] is a multilevel diffusion-based algorithm ... |

31 | Quality matching and local improvement for multilevel graph-partitioning
- Monien, Preis, et al.
- 1999
(Show Context)
Citation Context ... methods are based on mostly graph theoretic aspects, in particular edge contraction and local search. There are many ways to create graph hierarchies such as matching-based schemes [12], [13], [14], =-=[15]-=-, [16] or variations thereof [17] and techniques similar to algebraic multigrid [18], [19], [20]. We refer the interested reader to the respective papers for more details. Well-known software packages... |

31 | Engineering multilevel graph partitioning algorithms, in:
- Sanders, Schulz
- 2011
(Show Context)
Citation Context ... the previous multilevel iteration down the hierarchy. In the graph partitioning context, the notion of V-cycles was introduced by Walshaw [33]. More recent work augmented them to more complex cycles =-=[34]-=-. These previous works use matching-based coarsening with cut edges not being matched (and hence cut edges are not contracted). Thus, a given partition on the finest level can be used as initial parti... |

27 | Distributed evolutionary graph partitioning.”
- Sanders, Schulz
- 2012
(Show Context)
Citation Context ...mpute a graph clustering which is contracted. This is repeated until the graph is small enough. The coarsest graph is then partitioned by the coarse-grained distributed evolutionary algorithm KaFFPaE =-=[6]-=-. During uncoarsening the size-constraint label propagation algorithm is used as a simple, yet effective, parallel local search algorithm. The presented scheme speeds up computations and improves solu... |

25 | Balanced label propagation for partitioning massive graphs.
- Ugander, Backstrom
- 2013
(Show Context)
Citation Context ... ours. The label propagation clustering algorithm was initially proposed by Raghavan et al. [26]. Moreover, the label propagation algorithm has been used to partition networks by Uganer and Backstrom =-=[27]-=-. The authors do not use a multilevel scheme and rely on a given or random partition which are improved by combining the unconstrained label propagation approach with linear programming. Hence, the ap... |

24 | From “think like a vertex” to “think like a graph
- Tian, Balmin, et al.
(Show Context)
Citation Context ...r of blocks equals the number of processors used. PDiBaP [24] is a multilevel diffusion-based algorithm that is targeted at small to medium scale parallelism with dozens of processors. As reported by =-=[25]-=-, most large-scale graph processing toolkits based on cloud computing use ParMetis or rather straightforward partitioning strategies such as hash-based partitioning. While hashing often leads to accep... |

14 |
Stress-calculation in frameworks by the method of “Systematic relaxation of constraints
- Southwell
- 1935
(Show Context)
Citation Context ...at are able to obtain good partitions for large real-world graphs are based on the multilevel principle. The basic idea can be traced back to multigrid solvers for solving systems of linear equations =-=[11]-=- but more recent practical methods are based on mostly graph theoretic aspects, in particular edge contraction and local search. There are many ways to create graph hierarchies such as matching-based ... |

12 | Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid
- Meyerhenke, Monien, et al.
- 2006
(Show Context)
Citation Context ... and local search. There are many ways to create graph hierarchies such as matching-based schemes [12], [13], [14], [15], [16] or variations thereof [17] and techniques similar to algebraic multigrid =-=[18]-=-, [19], [20]. We refer the interested reader to the respective papers for more details. Well-known software packages based on this approach include Chaco [12], Jostle [13], Metis [14], Party [15] and ... |

12 |
Ja-be-ja: A distributed algorithm for balanced graph partitioning
- Rahimian, Payberah, et al.
- 2013
(Show Context)
Citation Context ...ion approach with linear programming. Hence, the approach does not yield high quality partitionings. Another distributed algorithm for balanced graph partitioning has been proposed by Rahimian et al. =-=[28]-=-. The authors use random initializations as starting point for local search which is basically node swapping. However, if the initialization is not balanced, the final partition computed by the algori... |

11 |
Chaco: Software for Partitioning Graphs. http://www.cs.sandia.gov/ ~bahendr/chaco.html
- Hendrickson
(Show Context)
Citation Context ...e recent practical methods are based on mostly graph theoretic aspects, in particular edge contraction and local search. There are many ways to create graph hierarchies such as matching-based schemes =-=[12]-=-, [13], [14], [15], [16] or variations thereof [17] and techniques similar to algebraic multigrid [18], [19], [20]. We refer the interested reader to the respective papers for more details. Well-known... |

11 | Advanced Coarsening Schemes for Graph Partitioning.
- Safro
- 2012
(Show Context)
Citation Context ...earch. There are many ways to create graph hierarchies such as matching-based schemes [12], [13], [14], [15], [16] or variations thereof [17] and techniques similar to algebraic multigrid [18], [19], =-=[20]-=-. We refer the interested reader to the respective papers for more details. Well-known software packages based on this approach include Chaco [12], Jostle [13], Metis [14], Party [15] and Scotch [16].... |

9 |
Graph partitioning and constructing optimal decision trees are polynomial complete problems
- Hyafil, Rivest
- 1973
(Show Context)
Citation Context ...ghboring nodes [2], but minimizing the cut size has been adopted as a kind of standard since it is usually highly correlated with the other formulations. The graph partitioning problem is NP-complete =-=[3]-=-, [4] and there is no approximation algorithm with a constant ratio factor for general graphs [5]. Hence, heuristic algorithms are used in practice. A successful heuristic for partitioning large graph... |

9 | Partitioning complex networks via size-constrained clustering,”
- Meyerhenke, Sanders, et al.
- 2014
(Show Context)
Citation Context ...y solutions. We organize the paper as follows. We begin in Section II by introducing basic concepts and outlining related work. Section III reviews the recently proposed cluster contraction algorithm =-=[7]-=- to partition complex networks, which is parallelized in this work. The main part of the paper is Section IV, which covers the parallelization of the size-constrained label propagation algorithm, the ... |

9 |
Graph Partitioning
- Bichot, Siarry
- 2011
(Show Context)
Citation Context ...h before and after a (un)contraction in the multilevel scheme throughout this paper. B. Related Work There has been a huge amount of research on graph partitioning so that we refer the reader to [8], =-=[9]-=-, [10] for most of the material. Here, we focus on issues closely related to our main contributions. All general-purpose methods that are able to obtain good partitions for large real-world graphs are... |

9 | Comparison of coarsening schemes for multilevel graph partitioning
- Chevalier, Safro
- 2009
(Show Context)
Citation Context ...ocal search. There are many ways to create graph hierarchies such as matching-based schemes [12], [13], [14], [15], [16] or variations thereof [17] and techniques similar to algebraic multigrid [18], =-=[19]-=-, [20]. We refer the interested reader to the respective papers for more details. Well-known software packages based on this approach include Chaco [12], Jostle [13], Metis [14], Party [15] and Scotch... |

7 | An ensemble learning strategy for graph clustering.
- Ovelgönne, Geyer-Schulz
- 2012
(Show Context)
Citation Context ...ble. It will be very interesting to generalize our algorithm for graph clustering w.r.t. modularity. For example, it should be straightforward to integrate the algorithm of Ovelgönne and Geyer-Schulz =-=[45]-=- to compute a high quality modularity graph clustering on the coarsest level of the hierarchy. This would enable researchers to compute graph clusterings of huge unstructured graphs in a short amount ... |

3 |
Scalable Parallel Graph Partitioning
- Kirmani, Raghavan
- 2013
(Show Context)
Citation Context ...alization is not balanced, the final partition computed by the algorithm will also be imbalanced and the largest graph under consideration has less than 70K nodes. Recent work by Kirmani and Raghavan =-=[29]-=- solves a relaxed version of the graph partitioning problem where no strict balance constraint is enforced. The blocks only have to have approximately the same size. Thus the problem is easier than th... |

2 | Shape Optimizing Load Balancing for MPI-Parallel Adaptive Numerical Simulations
- Meyerhenke
(Show Context)
Citation Context ...rent partitioning (band-refinement). KaPPa [23] is a parallel matching-based MGP algorithm which is also restricted to the case where the number of blocks equals the number of processors used. PDiBaP =-=[24]-=- is a multilevel diffusion-based algorithm that is targeted at small to medium scale parallelism with dozens of processors. As reported by [25], most large-scale graph processing toolkits based on clo... |

2 |
Act Globally: Highly Balanced Graph Partitioning
- Locally
- 2013
(Show Context)
Citation Context ...ultilevel graph drawing algorithm. Afterwards partitions are computed using a geometric scheme. 2 C. KaHIP Within this work, we use the open source multilevel graph partitioning framework KaHIP [30], =-=[31]-=- (Karlsruhe High Quality Partitioning). More precisely, we employ the distributed evolutionary algorithm KaFFPaE contained therein to create high quality partitions of complex networks at the coarsest... |

2 |
network analysis package (snap). http://snap.stanford.edu/. Accessed
- Leskovec
(Show Context)
Citation Context ...E I. BASIC PROPERTIES OF THE BENCHMARK SET WITH A ROUGH TYPE CLASSIFICATION. S STANDS FOR SOCIAL OR WEB GRAPHS, M IS USED FOR MESH TYPE NETWORKS. graph n m Type Ref. Large Graphs amazon ≈407K ≈2.3M S =-=[39]-=- eu-2005 ≈862K ≈16.1M S [36] youtube ≈1.1M ≈2.9M S [39] in-2004 ≈1.3M ≈13.6M S [36] packing ≈2.1M ≈17.4M M [36] enwiki ≈4.2M ≈91.9M S [41] channel ≈4.8M ≈42.6M M [36] hugebubble-10 ≈18.3M ≈27.5M M [36... |

1 | PT-Scotch
- Chevalier, Pellegrini
- 2008
(Show Context)
Citation Context ...ocessors. This parallelization has problems maintaining the balance of the partitions since at any particular time, it is difficult to say how many nodes are assigned to a particular block. PT-Scotch =-=[22]-=-, the parallel version of Scotch, is based on recursive bipartitioning. This is more difficult to parallelize than direct k-partitioning since in the initial bipartition, there is less parallelism ava... |

1 |
Benchmarking for Graph Clustering and Partitioning,” in Encyclopedia of Social Network Analysis and Mining
- Bader, Meyerhenke, et al.
(Show Context)
Citation Context ... BENCHMARK SET WITH A ROUGH TYPE CLASSIFICATION. S STANDS FOR SOCIAL OR WEB GRAPHS, M IS USED FOR MESH TYPE NETWORKS. graph n m Type Ref. Large Graphs amazon ≈407K ≈2.3M S [39] eu-2005 ≈862K ≈16.1M S =-=[36]-=- youtube ≈1.1M ≈2.9M S [39] in-2004 ≈1.3M ≈13.6M S [36] packing ≈2.1M ≈17.4M M [36] enwiki ≈4.2M ≈91.9M S [41] channel ≈4.8M ≈42.6M M [36] hugebubble-10 ≈18.3M ≈27.5M M [36] nlpkkt240 ≈27.9M ≈373M M [... |

1 |
Laboratory of Web Algorithms, “Datasets, http://law.dsi. unimi.it/datasets.php.” [Online]. Available: \url{http://law.dsi.unimi.it/ datasets.php
- M
(Show Context)
Citation Context ...TWORKS. graph n m Type Ref. Large Graphs amazon ≈407K ≈2.3M S [39] eu-2005 ≈862K ≈16.1M S [36] youtube ≈1.1M ≈2.9M S [39] in-2004 ≈1.3M ≈13.6M S [36] packing ≈2.1M ≈17.4M M [36] enwiki ≈4.2M ≈91.9M S =-=[41]-=- channel ≈4.8M ≈42.6M M [36] hugebubble-10 ≈18.3M ≈27.5M M [36] nlpkkt240 ≈27.9M ≈373M M [37] uk-2002 ≈18.5M ≈262M S [41] del26 ≈67.1M ≈201M M [23] rgg26 ≈67.1M ≈575M M [23] Larger Web Graphs arabic-2... |