Efficient Breadth-First Search on Massively Parallel and Distributed-Memory Machines

Ueno, K.; Suzumura, Toyotaro; Maruyama, Naoya; Matsuoka, Satoshi

doi:10.1007/s41019-016-0024-y

Cited by 26 publications

(8 citation statements)

References 16 publications

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“…There are two directions to improve our proposal. On one hand, the further speed-up technique will be established for coping with exascale graphs [46]. On the other hand, the extension to more complicated graph structures, such as dynamic graphs [21], and hypergraphs [22], will be investigated.…”

Section: Discussionmentioning

confidence: 99%

Distributed edge partitioning for trillion-edge graphs

et al. 2019

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We propose Distributed Neighbor Expansion (Distributed NE), a parallel and distributed graph partitioning method that can scale to trillion-edge graphs while providing high partitioning quality. Distributed NE is based on a new heuristic, called parallel expansion, where each partition is constructed in parallel by greedily expanding its edge set from a single vertex in such a way that the increase of the vertex cuts becomes local minimal. We theoretically prove that the proposed method has the upper bound in the partitioning quality. The empirical evaluation with various graphs shows that the proposed method produces higher-quality partitions than the state-of-the-art distributed graph partitioning algorithms. The performance evaluation shows that the space efficiency of the proposed method is an order-of-magnitude better than the existing algorithms, keeping its time efficiency comparable. As a result, Distributed NE can partition a trillion-edge graph using only 256 machines within 70 minutes.

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Section: Discussionmentioning

confidence: 99%

Distributed edge partitioning for trillion-edge graphs

et al. 2019

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“…Our technique of hiding or masking portions of A and the input vector could benefit new algebraic graph libraries that already feature masked sparse linear algebra operations [7,10,24,25], specifically for SpMmSpV. Since our method uses progressively smaller submatrices of A each step, it could prove useful in lowering the communication cost in distributed computing methods that bitmap and distribute partitions of the adjacency matrix [21]. Next we'll demonstrate how to easily integrate our method in the popular CSR format which is used in many sparse matrix libraries [12,15,22].…”

Section: J)mentioning

confidence: 99%

Optimal Algebraic Breadth-First Search for Sparse Graphs

Burkhardt

2021

ACM Trans. Knowl. Discov. Data

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There has been a rise in the popularity of algebraic methods for graph algorithms given the development of the GraphBLAS library and other sparse matrix methods. An exemplar for these approaches is Breadth-First Search (BFS). The algebraic BFS algorithm is simply a recurrence of matrix-vector multiplications with the n × n adjacency matrix, but the many redundant operations over nonzeros ultimately lead to suboptimal performance. Therefore an optimal algebraic BFS should be of keen interest especially if it is easily integrated with existing matrix methods. Current methods, notably in the GraphBLAS, use a Sparse Matrix masked-Sparse Vector multiplication in which the input vector is kept in a sparse representation in each step of the BFS, and nonzeros in the vector are masked in subsequent steps. This has been an area of recent research in GraphBLAS and other libraries. While in theory, these masking methods are asymptotically optimal on sparse graphs, many add work that leads to suboptimal runtime. We give a new optimal, algebraic BFS for sparse graphs, thus closing a gap in the literature. Our method multiplies progressively smaller submatrices of the adjacency matrix at each step. Let n and m refer to the number of vertices and edges, respectively. On a sparse graph, our method takes O ( n ) algebraic operations as opposed to O ( m ) operations needed by theoretically optimal sparse matrix approaches. Thus, for sparse graphs, it matches the bounds of the best-known sequential algorithm, and on a Parallel Random Access Machine, it is work-optimal. Our result holds for both directed and undirected graphs. Compared to a leading GraphBLAS library, our method achieves up to 24x faster sequential time, and for parallel computation, it can be 17x faster on large graphs and 12x faster on large-diameter graphs.

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“…RCM repeatedly marks all adjacent nodes of the current vertex, as shown in Algorithm 1. It is essentially a breadthfirst-search (BFS) algorithm, makes the tree deep enough to reduce the number of nodes in each layer in a disguised way, so as to reduce the bandwidth of the matrix [30], [31]. It is based on the CM method to sort the nodes in reverse order and take the smaller of the sum of the column heights in the positive order and the reverse order.…”

Section: ) Definitions and Notationsmentioning

confidence: 99%

Strength Check of Aircraft Parts Based on Multi-GPU Clusters for Fast Calculation of Sparse Linear Equations

Zhang

Hu²

2020

IEEE Access

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In order to improve the cost-effectiveness ratio, the next-generation vehicle needs to meet the requirements of reuse, while adopting a lighter structural weight, so it is necessary to realize the strength calculation and condition monitoring of key components in the digital twin. Most of the current monitoring methods are based on the characteristics of various data acquisition systems, but they need the support of a large number of flight data. The disadvantages of the above strategy can be avoided by reducing the structure of aircraft components to a finite element model and quickly checking the key components in the health management system. In order to solve the problem of fast calculation of the finite element model of the key components of the aircraft, a parallel algorithm and framework of large-scale sparse matrix preprocessing conjugate gradient method based on CUDA(Compute Unified Device Architecture) technology is proposed in the multi GPU(Graphics Processing Unit) workstation cluster environment. Once the sparse matrix is too large to be processed in a single workstation, this paper discusses how to realize the optimized data segmentation in the distributed multi-GPU computing environment. For the problem of iterative solution of matrix preprocessing, two preprocessing strategies of matrix bandwidth reduction parallelization and incomplete Cholesky decomposition are proposed, and asynchronous task concurrency and load balancing strategies are designed on the architecture. The calculation of some examples in the standard sparse matrix database shows that the algorithm and architecture proposed in this paper have the ability to solve large-scale sparse matrix quickly and efficiently, and can complete the fast strength verification of vehicle components.

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Efficient Breadth-First Search on Massively Parallel and Distributed-Memory Machines

Cited by 26 publications

References 16 publications

Distributed edge partitioning for trillion-edge graphs

Distributed edge partitioning for trillion-edge graphs

Optimal Algebraic Breadth-First Search for Sparse Graphs

Strength Check of Aircraft Parts Based on Multi-GPU Clusters for Fast Calculation of Sparse Linear Equations

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