Parallel triangle counting and k-truss identification using graph-centric methods

Voegele, Chad; Lu, Yi-Shan; Pai, Sreepathi; Pingali, Keshav

doi:10.1109/hpec.2017.8091037

Cited by 39 publications

(22 citation statements)

References 9 publications

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“…They present speedups to 23.6x on friendster graph with 72 threads. Regarding the k-truss decomposition, the HPEC challenge [35] attracted interesting studies that parallelize the computation [41,45,22]. In particular, Shaden et al [41] reports competitive results with respect to the earlier version of our work [36].…”

Section: Scalability and Comparison With Peelingmentioning

confidence: 74%

“…Our speedup numbers increase with more threads and faster solutions are possible with more cores. Recent results: There is a couple recent studies, concurrent to our work, that introduced new efficient parallel algorithms for k-core [8] and k-truss [41,45,22] decompositions. Dhulipala et al [8] have a new parallel bucket data structure for k-core decomposition that enables work-efficient parallelism, which is not possible with our algorithms.…”

Section: Scalability and Comparison With Peelingmentioning

confidence: 87%

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Local algorithms for hierarchical dense subgraph discovery

2018

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Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing these decompositions and the need for global information at each step of the algorithm hinders scalable parallelization and approximations since the densest regions are not revealed until the end. In a previous work, Lu et al. proposed to iteratively compute the h-indices of neighbor vertex degrees to obtain the core numbers and prove that the convergence is obtained after a finite number of iterations. This work generalizes the iterative h-index computation for truss decomposition as well as nucleus decomposition which leverages higher-order structures to generalize core and truss decompositions. In addition, we prove convergence bounds on the number of iterations. We present a framework of local algorithms to obtain the core, truss, and nucleus decompositions. Our algorithms are local, parallel, offer high scalability, and enable approximations to explore time and quality trade-offs. Our shared-memory implementation verifies the efficiency, scalability, and effectiveness of our local algorithms on real-world networks.

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Section: Scalability and Comparison With Peelingmentioning

confidence: 74%

Section: Scalability and Comparison With Peelingmentioning

confidence: 87%

Local algorithms for hierarchical dense subgraph discovery

2018

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“…Here, • denotes element-wise multiplication III. COMMUNITY SUBMISSIONS Graph Challenge 2017 received 22 submissions by 111 authors from 36 organizations [24]- [31], [34]- [41], [48]- [53]. The submissions were judged by a panel of experts on their effectiveness at using Graph Challenge to highlight innovations in graph algorithms, hardware, software, and systems.…”

Section: Triangle Countingmentioning

confidence: 99%

GraphChallenge.org: Raising the Bar on Graph Analytic Performance

Samsi¹,

Gadepally²,

Hurley³

et al. 2018

2018 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. Graph Challenge 2017 received 22 submissions by 111 authors from 36 organizations. The submissions highlighted graph analytic innovations in hardware, software, algorithms, systems, and visualization. These submissions produced many comparable performance measurements that can be used for assessing the current state of the art of the field. There were numerous submissions that implemented the triangle counting challenge and resulted in over 350 distinct measurements. Analysis of these submissions show that their execution time is a strong function of the number of edges in the graph, Ne, and is typically proportional to N 4/3 e for large values of Ne. Combining the model fits of the submissions presents a picture of the current state of the art of graph analysis, which is typically 10 8 edges processed per second for graphs with 10 8 edges. These results are 30 times faster than serial implementations commonly used by many graph analysts and underscore the importance of making these performance benefits available to the broader community. 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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“…There is currently significant research effort towards developing algorithms and systems capable of computing largescale triangle counting, participation, and enumeration. These efforts include implementations in MapReduce [25], [26], leveraging GPUs [18], [20], [27], in shared memory [28], utilizing linear algebraic kernels [29]- [32], and several other graph HPC implementations [12], [17], [33], [34]. A recent workshop, IEEE HPEC 2017 Graph Challenge [18], was organized to accelerate the progress of these efforts via crosscollaboration.…”

Section: Arxiv:180309021v1 [Csdm] 24 Mar 2018mentioning

confidence: 99%

On Large-Scale Graph Generation with Validation of Diverse Triangle Statistics at Edges and Vertices

Sanders¹,

Pearce²,

Fond³

et al. 2018

2018 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)

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Researchers developing implementations of distributed graph analytic algorithms require graph generators that yield graphs sharing the challenging characteristics of real-world graphs (small-world, scale-free, heavy-tailed degree distribution) with efficiently calculable ground-truth solutions to the desired output. Reproducibility for current generators [1] used in benchmarking are somewhat lacking in this respect due to their randomness: the output of a desired graph analytic can only be compared to expected values and not exact ground truth. Nonstochastic Kronecker product graphs [2] meet these design criteria for several graph analytics. Here we show that many flavors of triangle participation can be cheaply calculated while generating a Kronecker product graph.Given two medium-sized scale-free graphs with adjacency matrices A and B, their Kronecker product graph has adjacency matrix C = A ⊗ B. Such graphs are highly compressible: |E| edges are represented in O(|E| 1/2 ) memory and can be built in a distributed setting from small data structures, making them easy to share in compressed form. Many interesting graph calculations have worst-case complexity bounds O(|E| p ) and often these are reduced to O(|E| p/2 ) for Kronecker product graphs, when a Kronecker formula can be derived yielding the sought calculation on C in terms of related calculations on A and B.We focus on deriving formulas for triangle participation at vertices, tC , a vector storing the number of triangles that every vertex is involved in, and triangle participation at edges, ∆C , a sparse matrix storing the number of triangles at every edge. When factors A and B are undirected, C is also undirected. In the case when both factors have no self loops we show tC = 2tA ⊗ tB, ∆C = ∆A ⊗ ∆B. Moreover, we derive the respective formulas when A and B have self loops, which boosts the triangle counts for the associated vertices/edges in C. We additionally demonstrate strong assumptions on B that allow the truss decomposition of C to be derived cheaply from the truss decomposition of A.We extend these results and show Kronecker formulas for triangle participation in both directed graphs and undirected, vertex-labeled graphs. In these classes of graphs each vertex / edge can participate in many different types of triangles.

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Parallel triangle counting and k-truss identification using graph-centric methods

Cited by 39 publications

References 9 publications

Local algorithms for hierarchical dense subgraph discovery

Local algorithms for hierarchical dense subgraph discovery

GraphChallenge.org: Raising the Bar on Graph Analytic Performance

On Large-Scale Graph Generation with Validation of Diverse Triangle Statistics at Edges and Vertices

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