Practical parallel hypergraph algorithms

Shun, Julian

doi:10.1145/3332466.3374527

Cited by 38 publications

(19 citation statements)

References 71 publications

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“…When constructing hypergraphs with ADNS dataset, we consider the domains as the hyperedges and IPs as vertices. Additionally, we ran our experiments with datasets curated in [38]. For these curated datasets, in particular, each hypergraph, constructed from the social network datasets such as com-Orkut and Friendster in Table IV, are materialized by running a community detection algorithm on the original dataset obtained from Stanford Large Network Dataset Collection (SNAP) [27].…”

Section: B Datasetmentioning

confidence: 99%

“…Shared-memory C++-based framework Hygra [38], and distributed-memory frameworks such as Chapel-based CHGL [19], Apache Spark-based MESH [13] and HyperX [20] presented a collection of efficient parallel algorithms for hypergraphs in their frameworks. These frameworks either rely on the original hypergraph or the expansion graphs of hypergraphs.…”

Section: Related Workmentioning

confidence: 99%

“…cost of each step of the high-order line graph framework with the LiveJournal dataset[38]. Clearly, soverlap computation (in bold) is the dominant stage in the process.…”

mentioning

confidence: 99%

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High-order Line Graphs of Non-uniform Hypergraphs: Algorithms, Applications, and Experimental Analysis

Liu¹,

Firoz²,

Aksoy³

et al. 2022

Preprint

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Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs relies on first performing a graph expansion -either based on the nodes (clique expansion), or on the edges (line graph) -and then running standard graph analytics on the resulting representative graph. However, this approach suffers from massive space complexity and high computational cost with increasing hypergraph size. Here, we present efficient, parallel algorithms to accelerate and reduce the memory footprint of higher-order graph expansions of hypergraphs. Our results focus on the edge-based s-line graph expansion, but the methods we develop work for higher-order clique expansions as well. To the best of our knowledge, ours is the first framework to enable hypergraph spectral analysis of a large dataset on a single sharedmemory machine. Our methods enable the analysis of datasets from many domains that previous graph-expansion-based models are unable to provide. The proposed s-line graph computation algorithms are orders of magnitude faster than state-of-the-art sparse general matrix-matrix multiplication methods, and obtain approximately 5 − 31× speedup over a prior state-of-the-art heuristic-based algorithm for s-line graph computation.

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Section: B Datasetmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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High-order Line Graphs of Non-uniform Hypergraphs: Algorithms, Applications, and Experimental Analysis

Liu¹,

Firoz²,

Aksoy³

et al. 2022

Preprint

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show abstract

“…ForkGraph extends the Ligra framework by including its APIs (application programming interfaces), graph access methods, and the graph storage. We choose Ligra because of its high performance and wide adoptions by lines of excellent works, including [15,17,50,53]. Another reason is that users can leverage the friendly programming interfaces in Ligra.…”

Section: System Architecturementioning

confidence: 99%

Cache-Efficient Fork-Processing Patterns on Large Graphs

Lu,

Sun,

Paul

et al. 2021

Preprint

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As large graph processing emerges, we observe a costly fork-processing pattern (FPP) common in many graph algorithms. The unique feature of the FPP is that it launches many independent queries from different source vertices on the same graph. For example, an algorithm in analyzing the network community profile can execute Personalized PageRanks that start from tens of thousands of source vertices at the same time. We study the efficiency of state-of-the-art graph processing systems on multi-core architectures, including Ligra, Gemini, and GraphIt. We find that those systems suffer from severe cache miss penalty because of the irregular and uncoordinated memory accesses in processing FPPs.In this paper, we propose ForkGraph, a cache-efficient FPP processing system on multi-core architectures. In order to improve the cache reuse, we divide the graph into partitions each sized of LLC (last-level cache) capacity, and the queries in an FPP are buffered and executed on the partition basis. We further develop efficient intra-and inter-partition execution strategies for efficiency. For intra-partition processing, since the graph partition fits into LLC, we propose to execute each graph query with efficient sequential algorithms (in contrast with parallel algorithms in existing parallel graph processing systems) and present an atomic-free query processing by consolidating contending operations to cache-resident graph partition. For inter-partition processing, we propose two designs, yielding and priority-based scheduling, to reduce redundant work in processing. Besides, we theoretically prove that ForkGraph performs the same amount of work, to within a constant factor, as the fastest known sequential algorithms in FPP queries processing, which is work efficient. Our evaluations on real-world graphs show that ForkGraph significantly outperforms state-of-the-art graph processing systems (including Ligra, Gemini, and GraphIt) with two orders of magnitude speedups.

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“…However, to support 'industrial scale' uses of string diagrams where modelisations are very large, there is a pressing need to ensure that operations for combining these structures are efficient. In this work, we define a string diagram representation inspired by the parallel programming literature (specifically [8,14]). Our data structure of choice is based on sparse adjacency matrices representing hypergraphs, and thus we call it HAR -hypergraph adjacency representation.…”

Section: Introductionmentioning

confidence: 99%

The Cost of Compositionality: A High-Performance Implementation of String Diagram Composition

Wilson¹,

Zanasi²

2021

Preprint

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String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much fewer attention has been given to their algorithmic properties, and efficient implementations of diagrammatic reasoning are almost an unexplored subject.This work intends to be a contribution in such direction. We introduce a data structure representing string diagrams in terms of adjacency matrices. This encoding has the key advantage of providing simple and efficient algorithms for composition and tensor product of diagrams. We demonstrate its effectiveness by showing that the complexity of the two operations is linear in the size of string diagrams. Also, as our approach is based on basic linear algebraic operations, we can take advantage of heavily optimised implementations, which we use to measure performances of string diagrammatic operations via several benchmarks.

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Practical parallel hypergraph algorithms

Cited by 38 publications

References 71 publications

High-order Line Graphs of Non-uniform Hypergraphs: Algorithms, Applications, and Experimental Analysis

High-order Line Graphs of Non-uniform Hypergraphs: Algorithms, Applications, and Experimental Analysis

Cache-Efficient Fork-Processing Patterns on Large Graphs

The Cost of Compositionality: A High-Performance Implementation of String Diagram Composition

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