Many real-world systems, such as social networks, rely on mining efficiently large graphs, with hundreds of millions of vertices and edges. This volume of information requires partitioning the graph across multiple nodes in a distributed system. This has a deep effect on performance, as traversing edges cut between partitions incurs a significant performance penalty due to the cost of communication. Thus, several systems in the literature have attempted to improve computational performance by enhancing graph partitioning, but they do not support another characteristic of real-world graphs: graphs are inherently dynamic, their topology evolves continuously, and subsequently the optimum partitioning also changes over time. In this work, we present the first system that dynamically repartitions massive graphs to adapt to structural changes. The system optimises graph partitioning to prevent performance degradation without using data replication. The system adopts an iterative vertex migration algorithm that relies on local information only, making complex coordination unnecessary. We show how the improvement in graph partitioning reduces execution time by over 50 , while adapting the partitioning to a large number of changes to the graph in three real-world scenarios.
The idea of partitioning the graph to minimise network communication is not new and it has inspired several techniques to co-locate neighbouring vertices in the same host @cite_18 @cite_20 @cite_3 @cite_38 @cite_23 @cite_41 @cite_26 . These approaches try to exploit the locality present in the graphs, whether due to the vertices being geographically close in social networks, close molecules establishing chemical bonds, or web pages related by topic or domain, by placing neighbouring vertices in the same partition. The parallel version of METIS @cite_6 , ParMETIS @cite_13 , leverages parallel processing for partitioning the graph, through multilevel k-way partitioning, adaptive re-partitioning, and parallel multi-constrained partitioning schemes, but requires a global view of the graph that greatly reduces its scalability @cite_22 . Other techniques have been explored that study graph properties projected onto a small subset of vertices @cite_2 @cite_26 . These may be effective in some particular contexts, but they are not broadly applicable.
@cite_38 @cite_18 @cite_26 @cite_22 @cite_41 @cite_3 @cite_6 @cite_23 @cite_2 @cite_13 @cite_20
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Graph partitioning requires the division of a graph's vertex set into k equally sized subsets s.t. some objective function is optimized. High-quality partitions are important for many applications, whose objective functions are often NP-hard to optimize. Most state-of-the-art graph partitioning libraries use a variant of the Kernighan-Lin (KL) heuristic within a multilevel framework. While these libraries are very fast, their solutions do not always meet all user requirements. Moreover, due to its sequential nature, KL is not easy to parallelize. Its use as a load balancer in parallel numerical applications therefore requires complicated adaptations. That is why we developed previously an inherently parallel algorithm, called Bubble-FOS C [H. Meyerhenke, B. Monien, S. Schamberger, Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid, in: Proceedings of the 20th IEEE International Parallel and Distributed Processing Symposium, IPDPS'06, IEEE Computer Society, 2006, p. 57 (CD)], which optimizes partition shapes by a diffusive mechanism. However, it is too slow for practical use, despite its high solution quality. In this paper, besides proving that Bubble-FOS C converges towards a local optimum of a potential function, we develop a much faster method for the improvement of partitionings. This faster method called TruncCons is based on a different diffusive process, which is restricted to local areas of the graph and also contains a high degree of parallelism. By coupling TruncCons with Bubble-FOS C in a multilevel framework based on two different hierarchy construction methods, we obtain our new graph partitioning heuristic DibaP. Compared to Bubble-FOS C, DibaP shows a considerable acceleration, while retaining the positive properties of the slower algorithm. Experiments with popular benchmark graphs show that DibaP computes consistently better results than the state-of-the-art libraries METIS and JOSTLE. Moreover, with our new algorithm, we have improved the best known edge-cut values for a significant number of partitionings of six widely used benchmark graphs. The availability of larger and larger graph datasets, growing exponentially over the years, has created several new algorithmic challenges to be addressed. Sequential approaches have become unfeasible, while interest on parallel and distributed algorithms has greatly increased. Appropriately partitioning the graph as a preprocessing step can improve the degree of parallelism of its analysis. A number of heuristic algorithms have been developed to solve this problem, but many of them subdivide the graph on its vertex set, thus obtaining a vertex-partitioned graph. Aim of this paper is to explore a completely different approach based on edge partitioning, in which edges, rather than vertices, are partitioned into disjoint subsets. Contribution of this paper is twofold: first, we introduce a graph processing framework based on edge partitioning, that is flexible enough to be applied to several different graph problems. Second, we show the feasibility of these ideas by presenting a distributed edge partitioning algorithm called d-fep. Our framework is thoroughly evaluated, using both simulations and an Hadoop implementation running on the Amazon EC2 cloud. The experiments show that d-fep is efficient, scalable and obtains consistently good partitions. The resulting edge-partitioned graph can be exploited to obtain more efficient implementations of graph analysis algorithms. Balanced graph partitioning in the streaming setting is a key problem to enable scalable and efficient computations on massive graph data such as web graphs, knowledge graphs, and graphs arising in the context of online social networks. Two families of heuristics for graph partitioning in the streaming setting are in wide use: place the newly arrived vertex in the cluster with the largest number of neighbors or in the cluster with the least number of non-neighbors. In this work, we introduce a framework which unifies the two seemingly orthogonal heuristics and allows us to quantify the interpolation between them. More generally, the framework enables a well principled design of scalable, streaming graph partitioning algorithms that are amenable to distributed implementations. We derive a novel one-pass, streaming graph partitioning algorithm and show that it yields significant performance improvements over previous approaches using an extensive set of real-world and synthetic graphs. Surprisingly, despite the fact that our algorithm is a one-pass streaming algorithm, we found its performance to be in many cases comparable to the de-facto standard offline software METIS and in some cases even superiror. For instance, for the Twitter graph with more than 1.4 billion of edges, our method partitions the graph in about 40 minutes achieving a balanced partition that cuts as few as 6.8 of edges, whereas it took more than 81 2 hours by METIS to produce a balanced partition that cuts 11.98 of edges. We also demonstrate the performance gains by using our graph partitioner while solving standard PageRank computation in a graph processing platform with respect to the communication cost and runtime. The balanced graph partitioning consists in dividing the vertices of an undirected graph into a given number of subsets of approximately equal size, such that the number of edges crossing the subsets is minimized. In this work, we present a multilevel memetic algorithm for this NP-hard problem that relies on a powerful grouping recombination operator and a dedicated local search procedure. The proposed operator tends to preserve the backbone with respect to a set of parent individuals, i.e. the grouping of vertices which is same throughout each parent individual. Although our approach requires significantly longer computing time compared to some current state-of-art graph partitioning algorithms such as SCOTCH, METIS, CHACO, JOSTLE, etc., it competes very favorably with these approaches in terms of solution quality. Moreover, it easily reaches or improves on the best partitions ever reported in the literature.