Update on Triangle Counting on GPU

Pearson, Carl; Al-Masri, M.S.; Anjum, Omer; Mailthody, Vikram Sharma; Qureshi, Zaid; Nagi, Rakesh; Xiong, Jinjun; Hwu, Wen-mei W.

doi:10.1109/hpec.2019.8916547

Cited by 11 publications

(8 citation statements)

References 8 publications

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“…Triangle Counting. Many works perform triangle counting on the CPU [2,29,36,46] or the GPU [4,5,25,26,31,44,47,49,62,65]. A triangle is a 3-clique which is a special case of a 𝑘-clique.…”

Section: Related Workmentioning

confidence: 99%

“…List intersection is an important operation at the heart of many sub-graph search algorithms. Different list intersection strategies have been proposed for GPUs such as pointerchasing [3], binary-search [49], merge-path [26], hash-based [47], tile-based [15], bitmap-based [5], and others. Our implementations use binary-search intersections for extracting induced sub-graphs, and binary encoding for the lists in the induced sub-graph.…”

Section: Related Workmentioning

confidence: 99%

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Parallel K-clique counting on GPUs

Al-Masri

Hajj

Nagi

et al. 2022

Proceedings of the 36th ACM International Conference on Supercomputing

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Counting 𝑘-cliques in a graph is an important problem in graph analysis with many applications such as community detection and graph partitioning. Counting 𝑘-cliques is typically done by traversing search trees starting at each vertex in the graph. Parallelizing 𝑘-clique counting has been well-studied on CPUs and many solutions exist. However, there are no performant solutions for 𝑘-clique counting on GPUs.Parallelizing 𝑘-clique counting on GPUs comes with numerous challenges such as the need for extracting fine-grain multi-level parallelism, sensitivity to load imbalance, and constrained physical memory capacity. While there has been work on related problems such as finding maximal cliques and generalized sub-graph matching on GPUs, 𝑘-clique counting in particular has yet to be explored in depth. In this paper, we present the first parallel GPU solution specialized for the 𝑘-clique counting problem. Our solution supports both graph orientation and pivoting for eliminating redundant clique discovery. It incorporates both vertex-centric and edge-centric parallelization schemes for distributing work across thread blocks, and further partitions work within each thread block to extract fine-grain multi-level parallelism while tolerating load imbalance. It also includes optimizations such as binary encoding of induced sub-graphs and sub-warp partitioning to limit memory consumption and improve the utilization of execution resources.Our evaluation shows that our best GPU implementation outperforms the best state-of-the-art parallel CPU implementation by a geometric mean of 12.39×, 6.21×, and 18.99× for 𝑘 = 4, 7, and 10, respectively. We also perform a detailed evaluation of the trade-offs involved in the choice of parallelization scheme, and the incremental speedup of each optimization to provide an in-depth understanding of the optimization space. The insights from our optimization flow can be useful for optimizing other clique finding and graph mining solutions on GPUs. Our code will be open-sourced to enable further research on GPU parallelization of 𝑘-clique counting and other similar graph mining algorithms.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Parallel K-clique counting on GPUs

Al-Masri

Hajj

Nagi

et al. 2022

Proceedings of the 36th ACM International Conference on Supercomputing

Self Cite

View full text Add to dashboard Cite

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“…Mailthody et al [38] proposed a CPU-GPU collaborative algorithm for Triangle Counting and Truss Decomposition with UM. Pearson et al [50] utilized UM to simultaneous reading graph data from disk and construct graph in GPU memory with a double-buffering technique.…”

Section: Related Workmentioning

confidence: 99%

Grus

Wang

et al. 2021

ACM Trans. Archit. Code Optim.

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Today’s GPU graph processing frameworks face scalability and efficiency issues as the graph size exceeds GPU-dedicated memory limit. Although recent GPUs can over-subscribe memory with Unified Memory (UM), they incur significant overhead when handling graph-structured data. In addition, many popular processing frameworks suffer sub-optimal efficiency due to heavy atomic operations when tracking the active vertices. This article presents Grus, a novel system framework that allows GPU graph processing to stay competitive with the ever-growing graph complexity. Grus improves space efficiency through a UM trimming scheme tailored to the data access behaviors of graph workloads. It also uses a lightweight frontier structure to further reduce atomic operations. With easy-to-use interface that abstracts the above details, Grus shows up to 6.4× average speedup over the state-of-the-art in-memory GPU graph processing framework. It allows one to process large graphs of 5.5 billion edges in seconds with a single GPU.

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“…In 2018, eighteen submissions were selected for publication [84]- [101] and nine provided sufficient triangle counting performance data for analysis [84]- [92]. In 2019, twenty submissions were selected for publication [102]- [121] and eight provided sufficient triangle counting performance data for analysis [102]- [109].…”

Section: Triangle Countingmentioning

confidence: 99%

GraphChallenge.org Triangle Counting Performance

Samsi

Kepner

Gadepally

et al. 2020

2020 IEEE High Performance Extreme Computing Conference (HPEC)

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The rise of graph analytic systems has created a need for new ways to measure and compare the capabilities of graph processing systems. The MIT/Amazon/IEEE Graph Challenge has been developed to provide a well-defined community venue for stimulating research and highlighting innovations in graph analysis software, hardware, algorithms, and systems. GraphChallenge.org provides a wide range of preparsed graph data sets, graph generators, mathematically defined graph algorithms, example serial implementations in a variety of languages, and specific metrics for measuring performance. The triangle counting component of GraphChallenge.org tests the performance of graph processing systems to count all the triangles in a graph and exercises key graph operations found in many graph algorithms. In 2017, 2018, and 2019 many triangle counting submissions were received from a wide range of authors and organizations. This paper presents a performance analysis of the best performers of these submissions. These submissions show that their state-of-the-art triangle counting execution time, Ttri, is a strong function of the number of edges in the graph, Ne, which improved significantly from 2017 (Ttri ≈ (Ne/10 8 ) 4/3 ) to 2018 (Ttri ≈ Ne/10 9 ) and remained comparable from 2018 to 2019. Graph Challenge provides a clear picture of current graph analysis systems and underscores the need for new innovations to achieve high performance on very large graphs.

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Update on Triangle Counting on GPU

Cited by 11 publications

References 8 publications

Parallel K-clique counting on GPUs

Parallel K-clique counting on GPUs

Grus

GraphChallenge.org Triangle Counting Performance

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