Parallel triangle counting in massive streaming graphs

Tangwongsan, Kanat; Pavan, A.; Tirthapura, Srikanta

doi:10.1145/2505515.2505741

Cited by 60 publications

(24 citation statements)

References 31 publications

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“…In a follow-up work, we show that neighborhood sampling is amendable to parallelization. We have implemented a (provably) cache-efficient multicore parallel algorithm for approximate triangle counting where arbitrarily-ordered edges arrive in bulk [20].…”

Section: Resultsmentioning

confidence: 99%

Counting and sampling triangles from a graph stream

2013

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This paper presents a new space-efficient algorithm for counting and sampling triangles-and more generally, constant-sized cliques-in a massive graph whose edges arrive as a stream. Compared to prior work, our algorithm yields significant improvements in the space and time complexity for these fundamental problems. Our algorithm is simple to implement and has very good practical performance on large graphs.

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Section: Resultsmentioning

confidence: 99%

Counting and sampling triangles from a graph stream

2013

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“…There have also been various methods for approximating subgraph counts via sampling [34,3,4,63,32,13,50,42]. Finally, there has also been significant work for the past decade on parallel triangle counting algorithms (e.g., [56,7,57,6,46,47,15,45,58,60,39,35,26,25,30,19,28,65] and papers from the annual GraphChallenge [24], among many others).…”

Section: Related Workmentioning

confidence: 99%

Parallel Algorithms for Butterfly Computations

Shi

Shun

2020

Symposium on Algorithmic Principles of Computer Systems

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Butterflies are the smallest non-trivial subgraph in bipartite graphs, and therefore having efficient computations for analyzing them is crucial to improving the quality of certain applications on bipartite graphs. In this paper, we design a framework called ParButterfly that produces new parallel algorithms for the following problems on processing butterflies: global counting, per-vertex counting, per-edge counting, tip decomposition (vertex peeling), and wing decomposition (edge peeling). The main component of these algorithms is combining wedges incident on subsets of vertices, and our framework allows us to use different methods for wedge aggregation, including combining via sorting, hashing, histogramming, and batching. Moreover, ranking the vertices can speed up butterfly counting, as we only need to consider wedges formed by a particular ordering of the vertices. ParButterfly supports different ways to rank the vertices, including side ordering, approximate and exact degree ordering, and approximate and exact complement coreness ordering. For counting, ParButterfly also supports both exact computation as well as approximate computation via graph sparsification. We prove strong theoretical guarantees on the work and give parallel running times of the algorithms as obtained in our framework.We perform a comprehensive evaluation of all of the algorithms obtained from ParButterfly on a collection of real-world bipartite graphs using a 48-core machine. Our algorithms obtain significant parallel speedup, outperforming the fastest sequential algorithms by up to 13.6x with a self-relative speedup of up to 38.5x. Compared to general subgraph counting solutions, we are orders of magnitude faster. arXiv:1907.08607v1 [cs.DC] 19 Jul 2019 2 The arboricity of a graph is defined to be the minimum number of disjoint forests that a graph can be partitioned into.

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“…For now, it suffices to say that existing algorithms [5,12,20,28,2] will give different estimates for triangle counts of different multigraphs streams that contain the same simple graph. This is demonstrated in Fig.…”

Section: Triangle Countingmentioning

confidence: 99%

Counting triangles in real-world graph streams: Dealing with repeated edges and time windows

Jha¹,

Pınar

Seshadhri

2015

2015 49th Asilomar Conference on Signals, Systems and Computers

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Real-world graphs often manifest as a massive temporal "stream" of edges. The need for real-time analysis of such large graph streams has led to progress on low memory, one-pass streaming graph algorithms. These algorithms were designed for simple graphs, assuming an edge is not repeated in the stream. Real graph streams however, are almost always multigraphs i.e., they contain many duplicate edges. The assumption of no repeated edges requires an extra pass storing all the edges just for deduplication, which defeats the purpose of small memory algorithms.We describe an algorithm, MG-Triangle, for estimating the triangle count of a multigraph stream of edges. We show that all previous streaming algorithms for triangle counting fail for multigraph streams, despite their impressive accuracies for simple graphs. The bias created by duplicate edges is a major problem, and leads these algorithms astray. MG-Triangle avoids these biases through careful debiasing strategies and has provable theoretical guarantees and excellent empirical performance. MG-Triangle builds on the previously introduced wedge sampling methodology. Another challenge in analyzing temporal graphs is finding the right temporal window size. MG-Triangle seamlessly handles multiple time windows, and does not require committing to any window size(s) a priori. We apply MGTriangle to discover fascinating transitivity and triangle trends in real-world graph streams.

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Parallel triangle counting in massive streaming graphs

Cited by 60 publications

References 31 publications

Counting and sampling triangles from a graph stream

Counting and sampling triangles from a graph stream

Parallel Algorithms for Butterfly Computations

Counting triangles in real-world graph streams: Dealing with repeated edges and time windows

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