In the recent years, the scale of graph datasets has increased to such a degree that a single machine is not capable of efficiently processing large graphs. Thereby, efficient graph partitioning is necessary for those large graph applications. Traditional graph partitioning generally loads the whole graph data into the memory before performing partitioning; this is not only a time consuming task but it also creates memory bottlenecks. These issues of memory limitation and enormous time complexity can be resolved using stream-based graph partitioning. A streaming graph partitioning algorithm reads vertices once and assigns that vertex to a partition accordingly. This is also called an one-pass algorithm. This paper proposes an efficient window-based streaming graph partitioning algorithm called WStream. The WStream algorithm is an edge-cut partitioning algorithm, which distributes a vertex among the partitions. Our results suggest that the WStream algorithm is able to partition large graph data efficiently while keeping the load balanced across different partitions, and communication to a minimum. Evaluation results with real workloads also prove the effectiveness of our proposed algorithm, and it achieves a significant reduction in load imbalance and edge-cut with different ranges of dataset.
Stanton @cite_3 proposed a few heuristics for partitioning a large-scale graph in a streaming manner. Linear Deterministic Greedy (LDG) was the best performing heuristic of those heuristics. This algorithm is a Greedy heuristic, which is linear. It has a central graph loader, which loads and distributes data among the available workers. The heuristic assigns a vertex to the partition with which it shares the most edges. The algorithm was evaluated using 21 different static datasets and up to 16 partitions. It makes heuristics scale with the size and number of graph partitions. Based on PageRank computations, the method yielded a significant speed up achievement for large social networks by 18 The LDG algorithm is a well established streaming graph partitioning algorithm and is a state-of-the-art one-pass edge-cut partitioning algorithm. Therefore, in this study, we compared our one-pass edge-cut partitioning algorithm with the LDG algorithm @cite_3 .
@cite_3
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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. Extracting knowledge by performing computations on graphs is becoming increasingly challenging as graphs grow in size. A standard approach distributes the graph over a cluster of nodes, but performing computations on a distributed graph is expensive if large amount of data have to be moved. Without partitioning the graph, communication quickly becomes a limiting factor in scaling the system up. Existing graph partitioning heuristics incur high computation and communication cost on large graphs, sometimes as high as the future computation itself. Observing that the graph has to be loaded into the cluster, we ask if the partitioning can be done at the same time with a lightweight streaming algorithm. We propose natural, simple heuristics and compare their performance to hashing and METIS, a fast, offline heuristic. We show on a large collection of graph datasets that our heuristics are a significant improvement, with the best obtaining an average gain of 76 . The heuristics are scalable in the size of the graphs and the number of partitions. Using our streaming partitioning methods, we are able to speed up PageRank computations on Spark, a distributed computation system, by 18 to 39 for large social networks. 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. Partitioning of circuit netlists in VLSI design is considered. It is shown that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost. It is also demonstrated that fast Lanczos-type methods for the sparse symmetric eigenvalue problem are a robust basis for computing heuristic ratio cuts based on the eigenvector of this second eigenvalue. Effective clustering methods are an immediate by-product of the second eigenvector computation and are very successful on the difficult input classes proposed in the CAD literature. The intersection graph representation of the circuit netlist is considered, as a basis for partitioning, a heuristic based on spectral ratio cut partitioning of the netlist intersection graph is proposed. The partitioning heuristics were tested on industry benchmark suites, and the results were good in terms of both solution quality and runtime. Several types of algorithmic speedups and directions for future work are discussed. >