Counting the frequency of subgraphs in large networks is a classic research question that reveals the underlying substructures of these networks for important applications. However, subgraph counting is a challenging problem, even for subgraph sizes as small as five, due to the combinatorial explosion in the number of possible occurrences. This article focuses on the five-cycle, which is an important special case of five-vertex subgraph counting and one of the most difficult to count efficiently. We design two new parallel five-cycle counting algorithms and prove that they are work efficient and achieve polylogarithmic span. Both algorithms are based on computing low out-degree orientations, which enables the efficient computation of directed two-paths and three-paths, and the algorithms differ in the ways in which they use this orientation to eliminate double-counting. Additionally, we present new parallel algorithms for obtaining unbiased estimates of five-cycle counts using graph sparsification. We develop fast multicore implementations of the algorithms and propose a work scheduling optimization to improve their performance. Our experiments on a variety of real-world graphs using a 36-core machine with two-way hyper-threading show that our best exact parallel algorithm achieves 10–46× self-relative speedup, outperforms our serial benchmarks by 10–32×, and outperforms the previous state-of-the-art serial algorithm by up to 818×. Our best approximate algorithm, for a reasonable probability parameter, achieves up to 20× self-relative speedup and is able to approximate five-cycle counts 9–189× faster than our best exact algorithm, with between 0.52% and 11.77% error.
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A parallel algorithm for generating a random graph with a prescribed degree sequence
Random graphs (or networks) have gained a significant increase of interest due to its popularity in modeling and simulating many complex real-world systems. Degree sequence is one of the most important aspects of these systems. Random graphs with a given degree sequence can capture many characteristics like dependent edges and non-binomial degree distribution that are absent in many classical random graph models such as the Erdöos-Rényi graph model. In addition, they have important applications in uniform sampling of random graphs, counting the number of graphs having the same degree sequence, as well as in string theory, random matrix theory, and matching theory. In this paper, we present an OpenMP-based shared-memory parallel algorithm for generating a random graph with a prescribed degree sequence, which achieves a speedup of 20.4 with 32 cores. We also present a comparative study of several structural properties of the random graphs generated by our algorithm with that of the real-world graphs and random graphs generated by other popular methods. One of the steps in our parallel algorithm requires checking the Erdöos-Gallai characterization, i.e., whether there exists a graph obeying the given degree sequence, in parallel. This paper presents a non-trivial parallel algorithm for checking the Erdöos-Gallai characterization, which achieves a speedup of 23 with 32 cores.
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- Award ID(s):
- 1633028
- NSF-PAR ID:
- 10067732
- Date Published:
- Journal Name:
- 2017 IEEE International Conference on Big Data (Big Data)
- Page Range / eLocation ID:
- 3312 to 3321
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/BigData.2017.8258316
