Fast Parallel Graph Triad Census and Triangle Counting on Shared-Memory Platforms

Parimalarangan, Sindhuja; Slota, George M.; Madduri, Kamesh

doi:10.1109/ipdpsw.2017.144

Cited by 10 publications

(8 citation statements)

References 37 publications

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“…Compared to truss decomposition, triangle counting is a very well-studied problem. We refer readers to [26], [27], [28], [29], [30], [31], [32] for a sampling of efficient algorithms and practical high-performance implementations. Xiao et al [31] unify a large body of previously-developed triangle counting algorithms and observe that the ordering of vertices and orientation of edges has a significant impact on performance.…”

Section: Introductionmentioning

confidence: 99%

Shared-Memory Graph Truss Decomposition

Kabir

Madduri²

2017

2017 IEEE 24th International Conference on High Performance Computing (HiPC)

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We present PKT, a new shared-memory parallel algorithm and OpenMP implementation for the truss decomposition of large sparse graphs. A k-truss is a dense subgraph definition that can be considered a relaxation of a clique. Truss decomposition refers to a partitioning of all the edges in the graph based on their k-truss membership. The truss decomposition of a graph has many applications. We show that our new approach PKT consistently outperforms other truss decomposition approaches for a collection of large sparse graphs and on a 24-core shared-memory server. PKT is based on a recently proposed algorithm for k-core decomposition.

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Section: Introductionmentioning

confidence: 99%

Shared-Memory Graph Truss Decomposition

Kabir

Madduri²

2017

2017 IEEE 24th International Conference on High Performance Computing (HiPC)

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“…This is because for each v i , the hash-map used to store the adjacency list of v i can be reused for all v j ∈ U i, * . The list-based and map-based methods are further detailed in [13,19,21].…”

Section: Background 31 Triangle Countingmentioning

confidence: 99%

“…In recent years, driven by the growing size of the graphs that needs to be analyzed, there has been significant research in improving the efficiency of parallel algorithms for computing the exact and approximate number of triangles. Parallel triangle counting algorithms have been specifically built for GPUs, external memory, shared-memory, and distributed-memory platforms [1,2,7,8,13,16,19,23,25]. The shared-memory class of solutions are limited by the amount of memory that is available in a single processor, thus, limiting the size of the graphs that can be analyzed.…”

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confidence: 99%

A 2D Parallel Triangle Counting Algorithm for Distributed-Memory Architectures

Tom

Karypis

2019

Proceedings of the 48th International Conference on Parallel Processing

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Triangle counting is a fundamental graph analytic operation that is used extensively in network science and graph mining. As the size of the graphs that needs to be analyzed continues to grow, there is a requirement in developing scalable algorithms for distributedmemory parallel systems. To this end, we present a distributedmemory triangle counting algorithm, which uses a 2D cyclic decomposition to balance the computations and reduce the communication overheads. The algorithm structures its communication and computational steps such that it reduces its memory overhead and includes key optimizations that leverage the sparsity of the graph and the way the computations are structured. Experiments on synthetic and real-world graphs show that our algorithm obtains an average relative speedup range between 3.24 to 7.22 out of 10.56 across the datasets using 169 MPI ranks over the performance achieved by 16 MPI ranks. Moreover, we obtain an average speedup of 10.2 times on comparison with previously developed distributed-memory parallel algorithms.

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“…The paper shows that these algorithms can achieve better cache utilization. Madduri et al [21] presented variations of triangle counting algorithms and how they related to performance in shared-memory platforms. [28] also discuss number of optimizations to speedup sequential and shared-memory parallel triangle counting algorithms.…”

Section: Related Workmentioning

confidence: 99%

“…However, processing every wedge in a separate parallel thread reduces the cache utilization and also increases the number of messages in distributed execution. A common optimization to reduce the number of processing wedges is to order vertices by their degree (e.g., [21]). Applying this optimization as it is for distributed, shared-memory triangle counting is challenging.…”

Section: Introductionmentioning

confidence: 99%

Distributed, Shared-Memory Parallel Triangle Counting

Kanewala

Zalewski

Lumsdaine

2018

Proceedings of the Platform for Advanced Scientific Computing Conference

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Triangles are the most basic non-trivial subgraphs. Triangle counting is used in a number of different applications, including social network mining, cyber security, and spam detection. In general, triangle counting algorithms are readily parallelizable, but when implemented in distributed, shared-memory, their performance is poor due to high communication, imbalance of work, and the difficulty of exploiting locality available in shared memory. In this paper, we discuss four different (but related) triangle counting algorithms and how their performance can be improved in distributed, shared-memory by reducing in-node load imbalance, improving cache utilization, minimizing network overhead, and minimizing algorithmic work. We generalize the four different triangle counting algorithms into a common framework and show that for all four algorithms the in-node load imbalance can be minimized while utilizing caches by partitioning work into blocks of vertices, the network overhead can be minimized by aggregation of blocks of work, and algorithm work can be reduced by partitioning vertex neighbors by degree.We experimentally evaluate the weak and the strong scaling performance of the proposed algorithms with two types of synthetic graph inputs and three real-world graph inputs. We also compare the performance of our implementations with the distributed, shared-memory triangle counting algorithms available in PowerGraph-GraphLab and show that our proposed algorithms outperform those algorithms, both in terms of space and time.

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Fast Parallel Graph Triad Census and Triangle Counting on Shared-Memory Platforms

Cited by 10 publications

References 37 publications

Shared-Memory Graph Truss Decomposition

Shared-Memory Graph Truss Decomposition

A 2D Parallel Triangle Counting Algorithm for Distributed-Memory Architectures

Distributed, Shared-Memory Parallel Triangle Counting

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