Logarithmic Radix Binning and Vectorized Triangle Counting

Green, Oded; Fox, James; Watkins, Alex; Tripathy, Aruna; Gabert, Kasimir; Kim, Eun-A; An, Xiaojing; Aatish, Kumar; Bader, David A.

doi:10.1109/hpec.2018.8547581

Cited by 18 publications

(8 citation statements)

References 22 publications

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“…These load-balancing mechanisms work at various parallel granularities, ranging from the warps and all the up-to-the whole device. Logarithmic Radix Binning (LRB) is a load-balancing mechanism first introduced in [23,26] for triangle counting and later generalized for other graph problems and segmented sorting [24]. Our ButterFly BFS algorithm uses LRB for performance purposes.…”

Section: Related Workmentioning

confidence: 99%

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ButterFly BFS -- An Efficient Communication Pattern for Multi Node Traversals

Green¹

2021

Preprint

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Breadth-First Search (BFS) is a building block used in a wide array of graph analytics and is used in various network analysis domains: social, road, transportation, communication, and much more. Over the last two decades, network sizes have continued to grow. The popularity of BFS has brought with it a need for significantly faster traversals. Thus, BFS algorithms have been designed to exploit shared-memory and shared-nothing systems-this includes algorithms for accelerators such as the GPU. GPUs offer extremely fast traversals at the cost of processing smaller graphs due to their limited memory size. In contrast, CPU shared-memory systems can scale to graphs with several billion edges but do not have enough compute resources needed for fast traversals. This paper introduces ButterFly BFS, a multi-GPU traversal algorithm that allows analyzing significantly larger networks at high rates. ButterFly BFS scales to the similar-sized graphs processed by shared-memory systems while improving performance by more than 10X compared to CPUs. We evaluate our new algorithm on an NVIDIA DGX-2 server with 16 V100 GPUS and show that our algorithm scales with an increase in the number of GPUS. We show that we can achieve a roughly 70% performance linear speedup, which is non-trivial for BFS. For a scale 29 Kronecker graph and edge factor of 8, our new algorithm traverses the graph at a rate of over 300 GTEP/s. That is a high traversal rate for a single server.

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Section: Related Workmentioning

confidence: 99%

“…Load Balanced Traversals Per compute-node. The BFS traversal on GPU uses the recent Logarithmic Radix Binning (LRB) technique discussed in [24,26]. LRB groups vertices in the frontier into roughly 32 bins or 64 bins, depending on the graphs' maximal number of vertices.…”

Section: Dgx-2mentioning

confidence: 99%

ButterFly BFS -- An Efficient Communication Pattern for Multi Node Traversals

Green¹

2021

Preprint

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Section: Device Primitives For Set Operationsmentioning

confidence: 99%

“…Previous work has explored set intersection on SIMD [10,15,46,52,120] or GPU [8,39,41,42,50,51,80,81,114,115]. We classify their algorithms into 3 categories: Merge-path [41,42], Binary-search [39,51] and Hash-indexing [81]. We have extensively evaluated these methods on GPU, and we find that binary-search works the best since it is less divergent.…”

Section: Device Primitives For Set Operationsmentioning

confidence: 99%

Efficient and Scalable Graph Pattern Mining on GPUs

Chen¹,

Arvind²

2021

Preprint

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We describe G 2 Miner, the first Graph Pattern Mining (GPM) framework that runs on multiple GPUs. G 2 Miner uses pattern-aware, input-aware and architecture-aware search strategies to achieve high efficiency on GPUs. To simplify programming, it provides a code generator that automatically generates pattern-aware CUDA code. G 2 Miner flexibly supports both breadth-first search (BFS) and depth-first search (DFS) to maximize memory utilization and generate sufficient parallelism for GPUs. For the scalability of G 2 Miner, we propose a customized scheduling policy to balance work among multiple GPUs. Experiments on a V100 GPU show that G 2 Miner is 5.4× and 7.2× faster than the two state-ofthe-art single-GPU systems, Pangolin and PBE, respectively. In the multi-GPU setting, G 2 Miner achieves linear speedups from 1 to 8 GPUs, for various patterns and data graphs. We also show that G 2 Miner on a V100 GPU is 48.3× and 15.2× faster than the state-of-the-art CPU-based systems, Peregrine and GraphZero, on a 56-core CPU machine.

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“…Motifs like triangles represent a quantum of cohesion in graphs and the number of motifs containing an entity (vertex or an edge) acts as an indicator of its local density. Consequently, several recent works have focused on efficiently finding such motifs in the graphs [1,16,22,25,35,54,56,66].…”

Section: Related Workmentioning

confidence: 99%

Parallel Peeling of Bipartite Networks for Hierarchical Dense Subgraph Discovery

Lakhotia¹,

Kannan²,

Prasanna³

2021

Preprint

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Motif-based graph decomposition is widely used to mine hierarchical dense structures in graphs. In bipartite graphs, wing and tip decomposition construct a hierarchy of butterfly (2,2-biclique) dense edge and vertex induced subgraphs, respectively. They have applications in several domains including e-commerce, recommendation systems and document analysis.Existing decomposition algorithms use a bottom-up approach that constructs the hierarchy in an increasing order of subgraph density. They iteratively select the entities (edges or vertices) with minimum support (butterfly count) and peel them i.e. remove them from them graph and update the support of other entities. The amount of butterflies in real-world bipartite graphs makes bottom-up peeling computationally demanding. Furthermore, the strict order of peeling entities results in a large number of iterations with sequential dependencies on preceding support updates. Consequently, parallel algorithms based on bottom up peeling can only utilize intra-iteration parallelism and require heavy synchronization, leading to poor scalability.In this paper, we propose a novel Parallel Bipartite Network peelinG (PBNG) framework which adopts a two-phased peeling approach to relax the order of peeling, and in turn, dramatically reduce synchronization. The first phase divides the decomposition hierarchy into few partitions, and requires little synchronization to compute such partitioning. The second phase concurrently processes all of these partitions to generate individual levels in the final decomposition hierarchy, and requires no global synchronization.Effectively, both phases of PBNG parallelize computation across multiple levels of decomposition hierarchy, which is not possible with bottom-up peeling. The two-phased peeling further enables batching optimizations that dramatically improve the computational efficiency of PBNG. The proposed approach represents a non-trivial generalization of our prior work on a two-phased vertex peeling algorithm [30], and its adoption for both tip and wing decomposition.We empirically evaluate PBNG using several real-world bipartite graphs and demonstrate radical improvements over the existing approaches. On a shared-memory 36 core server, PBNG achieves up to 19.7× self-relative parallel speedup. Compared to the state-of-theart parallel framework ParButterfly, PBNG reduces synchronization by up to 15260× and execution time by up to 295×. Furthermore, it achieves up to 38.5× speedup over state-of-the-art algorithms specifically tuned for wing decomposition. We also present the first decomposition results of some of the largest public real-world datasets, which PBNG can peel in few minutes/hours, but algorithms in current practice fail to process even in several days. Our source code is made available at https://github.com/kartiklakhotia/RECEIPT.

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Logarithmic Radix Binning and Vectorized Triangle Counting

Cited by 18 publications

References 22 publications

ButterFly BFS -- An Efficient Communication Pattern for Multi Node Traversals

ButterFly BFS -- An Efficient Communication Pattern for Multi Node Traversals

Efficient and Scalable Graph Pattern Mining on GPUs

Parallel Peeling of Bipartite Networks for Hierarchical Dense Subgraph Discovery

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