Parallel Algorithms for Finding Large Cliques in Sparse Graphs

Gianinazzi, Lukas; Besta, Maciej; Schaffner, Yannick; Hoefler, Torsten

doi:10.1145/3409964.3461800

Cited by 13 publications

(3 citation statements)

References 39 publications

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“…); Slota and Madduri, 2013). The goal is to find topologically well-defined motifs such as triangles and cliques (Gianinazzi et al, 2021) and k-truss (Kabir and Madduri, 2017) to identify the properties of the graph. Counting triangles are well studied as it estimates whether it is community-like.…”

Section: Subgraph Isomorphism and Its Variationsmentioning

confidence: 99%

A Survey of Graph Comparison Methods with Applications to Nondeterminism in High-Performance Computing

Bhowmick

Bell

Taufer

2023

The International Journal of High Performance Computing Applica

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The convergence of extremely high levels of hardware concurrency and the effective overlap of computation and communication in asynchronous executions has resulted in increasing nondeterminism in High-Performance Computing (HPC) applications. Nondeterminism can manifest at multiple levels: from low-level communication primitives to libraries to application-level functions. No matter its source, nondeterminism can drastically increase the cost of result reproducibility, debugging workflows, testing parallel programs, or ensuring fault-tolerance. Nondeterministic executions of HPC applications can be modeled as event graphs, and the applications’ nondeterministic behavior can be understood and, in some cases, mitigated using graph comparison algorithms. However, a connection between graph comparison algorithms and approaches to understanding nondeterminism in HPC still needs to be established. This survey article moves the first steps toward establishing a connection between graph comparison algorithms and nondeterminism in HPC with its three contributions: it provides a survey of different graph comparison algorithms and a timeline for each category’s significant works; it discusses how existing graph comparison methods do not fully support properties needed to understand nondeterministic patterns in HPC applications; and it presents the open challenges that should be addressed to leverage the power of graph comparisons for the study of nondeterminism in HPC applications.

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Section: Subgraph Isomorphism and Its Variationsmentioning

confidence: 99%

A Survey of Graph Comparison Methods with Applications to Nondeterminism in High-Performance Computing

Bhowmick

Bell

Taufer

2023

The International Journal of High Performance Computing Applica

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“…One avenue of future works lies in developing new HOGDMs beyond those in Table 1, which could better encapsulate HO interactions between entities in a way that is both computationally efficient and representative of the underlying complexities of the data. For example, one could consider novel substructures for Motif-Graphs, such as different forms of dense subgraphs [44], [49], [111], [113], [158], [173], [210].…”

Section: Research Opportunitiesmentioning

confidence: 99%

Motif Prediction with Graph Neural Networks

Besta¹,

Grob²,

Miglioli³

et al. 2022

Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining

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Link prediction is one of the central problems in graph mining. However, recent studies highlight the importance of higher-order network analysis, where complex structures called motifs are the first-class citizens. We first show that existing link prediction schemes fail to effectively predict motifs. To alleviate this, we establish a general motif prediction problem and we propose several heuristics that assess the chances for a specified motif to appear. To make the scores realistic, our heuristics consider -among others -correlations between links, i.e., the potential impact of some arriving links on the appearance of other links in a given motif. Finally, for highest accuracy, we develop a graph neural network (GNN) architecture for motif prediction. Our architecture offers vertex features and sampling schemes that capture the rich structural properties of motifs. While our heuristics are fast and do not need any training, GNNs ensure highest accuracy of predicting motifs, both for dense (e.g., 𝑘-cliques) and for sparse ones (e.g., 𝑘-stars). We consistently outperform the best available competitor by more than 10% on average and up to 32% in area under the curve. Importantly, the advantages of our approach over schemes based on uncorrelated link prediction increase with the increasing motif size and complexity. We also successfully apply our architecture for predicting more arbitrary clusters and communities, illustrating its potential for graph mining beyond motif analysis. CCS CONCEPTS• Information systems → Data mining.

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“…Graph Orientation Approach to Clique Counting. Graph orientation is a fundamental approach to avoiding redundant clique discovery [11,13,20,21,40,42,56]. To our knowledge, ARB-COUNT [56] is the state-of-the-art parallel implementation of 𝑘-clique counting on CPUs based on graph orientation.…”

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

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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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Parallel Algorithms for Finding Large Cliques in Sparse Graphs

Cited by 13 publications

References 39 publications

A Survey of Graph Comparison Methods with Applications to Nondeterminism in High-Performance Computing

A Survey of Graph Comparison Methods with Applications to Nondeterminism in High-Performance Computing

Motif Prediction with Graph Neural Networks

Parallel K-clique counting on GPUs

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