GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra

Besta, Maciej; Vonarburg-Shmaria, Zur; Schaffner, Yannick; Schwarz, Leonardo; Kwasniewski, Grzegorz; Gianinazzi, Lukas; Beránek, Jakub; Janda, Kacper; Holenstein, Tobias; Leisinger, Sebastian; Tatkowski, Peter; Ozdemir, Esref; Balla, Adrian; Copik, Marcin; Lindenberger, Philipp; Kalvoda, Pavel; Konieczny, Marek T.; Mutlu, Onur; Hoefler, Torsten

doi:10.48550/arxiv.2103.03653

Cited by 4 publications

(9 citation statements)

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“…Ballard et al [45] present an extensive collection of linear algebra algorithms. Moreover, a large body of work exists for minimizing communication in irregular algorithms [46,47], such as Betweenness Centrality [5], min cuts [48], BFS [49], matchings [50], vertex similarity coefficients [51], or general graph computations [52,53,53]. Many of them use linear algebra based formulations [54].…”

Section: Related Workmentioning

confidence: 99%

Pebbles, Graphs, and a Pinch of Combinatorics: Towards Tight I/O Lower Bounds for Statically Analyzable Programs

Kwasniewski,

Ben-Nun,

Gianinazzi

et al. 2021

Preprint

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Determining I/O lower bounds is a crucial step in obtaining communication-efficient parallel algorithms, both across the memory hierarchy and between processors. Current approaches either study specific algorithms individually, disallow programmatic motifs such as recomputation, or produce asymptotic bounds that exclude important constants. We propose a novel approach for obtaining precise I/O lower bounds on a general class of programs, which we call Simple Overlap Access Programs (SOAP). SOAP analysis covers a wide variety of algorithms, from ubiquitous computational kernels to full scientific computing applications. Using the red-blue pebble game and combinatorial methods, we are able to bound the I/O of the SOAP-induced Computational Directed Acyclic Graph (CDAG), taking into account multiple statements, input/output reuse, and optimal tiling. To deal with programs that are outside of our representation (e.g., non-injective access functions), we describe methods to approximate them with SOAP. To demonstrate our method, we analyze 38 different applications, including kernels from the Polybench benchmark suite, deep learning operators, and -for the first time -applications in unstructured physics simulations, numerical weather prediction stencil compositions, and full deep neural networks. We derive tight I/O bounds for several linear algebra kernels, such as Cholesky decomposition, improving the existing reported bounds by a factor of two. For stencil applications, we improve the existing bounds by a factor of up to 14. We implement our method as an open-source tool, which can derive lower bounds directly from provided C code.

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Section: Related Workmentioning

confidence: 99%

Pebbles, Graphs, and a Pinch of Combinatorics: Towards Tight I/O Lower Bounds for Statically Analyzable Programs

Kwasniewski,

Ben-Nun,

Gianinazzi

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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“…However, recent works argue the importance of higher-order graph organization [6], where one focuses on finding and analyzing small recurring subgraphs called motifs (sometimes referred to as graphlets or graph patterns) instead of individual links. Motifs are central to many graph mining problems in computational biology, chemistry, and a plethora of other fields [9,12,13,18,20,27,30]. Specifically, motifs are building blocks of different networks, including transcriptional regulation graphs, social networks, brain graphs, or air traffic patterns [6].…”

Section: Introductionmentioning

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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“…However, recent works argue the importance of higher-order graph organization [10], where one focuses on finding and analyzing small recurring subgraphs called motifs (sometimes referred to as graphlets or graph patterns) instead of individual links. Motifs are central to many graph mining problems in computational biology, chemistry, and a plethora of other fields [16,22,23,28,30,41,46]. Specifically, motifs are building blocks of different networks, including transcriptional regulation graphs, social networks, brain graphs, or air traffic patterns [10].…”

Section: Introductionmentioning

confidence: 99%

“…There exist many motifs, for example k-cliques, k-stars, k-clique-stars, k-cores, and others [20,43,54]. A huge number of works are dedicated to motif counting, listing (also called enumeration), or checking for the existence of a given motif [22,30]. However, while a few recent schemes focus on predicting triangles [9,63,64], no works target the problem of general motif prediction, i.e., analyzing whether specified complex structures may appear in the data.…”

Section: Introductionmentioning

confidence: 99%

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Motif Prediction with Graph Neural Networks

Besta¹,

Grob²,

Miglioli³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra

Cited by 4 publications

References 0 publications

Pebbles, Graphs, and a Pinch of Combinatorics: Towards Tight I/O Lower Bounds for Statically Analyzable Programs

Pebbles, Graphs, and a Pinch of Combinatorics: Towards Tight I/O Lower Bounds for Statically Analyzable Programs

Motif Prediction with Graph Neural Networks

Motif Prediction with Graph Neural Networks

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