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Networks (or graphs) are used to model the dyadic relations between entities in complex systems. Analyzing the properties of the networks reveal important characteristics of the underlying system. However, in many disciplines, including social sciences, bioinformatics, and technological systems, multiple relations exist between entities. In such cases, a simple graph is not sufficient to model these multiple relations, and a multilayer network is a more appropriate model. In this paper, we explore community detection in multilayer networks. Specifically, we propose a novel network decoupling strategy for efficiently combining the communities in the different layers using the Boolean primitives AND, OR, and NOT. Our proposed method, network decoupling, is based on analyzing the communities in each network layer individually and then aggregating the analysis results. We (i) describe our network decoupling algorithms for finding communities, (ii) present how network decoupling can be used to express different types of communities in multilayer networks, and (iii) demonstrate the effectiveness of using network decoupling for detecting communities in real-world and synthetic data sets. Compared to other algorithms for detecting communities in multilayer networks, our proposed network decoupling method requires significantly lower computation time while producing results of high accuracy. Based on these results, we anticipate that our proposed network decoupling technique will enable a more detailed analysis of multilayer networks in an efficient manner. 

The convergence of extremely high levels of hardware concurrency and the effective overlap of computation and communication in asynchronous executions has resulted in increasing nondeterminism in High-Performance Computing (HPC) applications. Nondeterminism can manifest at multiple levels: from low-level communication primitives to libraries to application-level functions. No matter its source, nondeterminism can drastically increase the cost of result reproducibility, debugging workflows, testing parallel programs, or ensuring fault-tolerance. Nondeterministic executions of HPC applications can be modeled as event graphs, and the applications’ nondeterministic behavior can be understood and, in some cases, mitigated using graph comparison algorithms. However, a connection between graph comparison algorithms and approaches to understanding nondeterminism in HPC still needs to be established. This survey article moves the first steps toward establishing a connection between graph comparison algorithms and nondeterminism in HPC with its three contributions: it provides a survey of different graph comparison algorithms and a timeline for each category’s significant works; it discusses how existing graph comparison methods do not fully support properties needed to understand nondeterministic patterns in HPC applications; and it presents the open challenges that should be addressed to leverage the power of graph comparisons for the study of nondeterminism in HPC applications. 

We present the first GPU-based parallel algorithm to efficiently update vertex coloring on large dynamic networks. For single GPU, we introduce the concept of loosely maintained vertex color update that reduces computation and memory requirements. For multiple GPUs, in distributed environments, we propose priority-based ordering of vertices to reduce the communication time. We prove the correctness of our algorithms and experimentally demonstrate that for graphs of over 16 million vertices and over 134 million edges on a single GPU, our dynamic algorithm is as much as 20x faster than state-of-the-art algorithm on static graphs. For larger graphs with over 130 million vertices and over 260 million edges, our distributed implementation with 8 GPUs produces updated color assignments within 160 milliseconds. In all cases, the proposed parallel algorithms produce comparable or fewer colors than state-of-the-art algorithms. 

We present EASEE (Edge Advertisements into Snapshots using Evolving Expectations) for partitioning streaming communication data into static graph snapshots. Given streaming communication events (A talks to B), EASEE identifies when events suffice for a static graph (a snapshot ). EASEE uses combinatorial statistical models to adaptively find when a snapshot is stable, while watching for significant data shifts – indicating a new snapshot should begin. If snapshots are not found carefully, they poorly represent the underlying data – and downstream graph analytics fail: We show a community detection example. We demonstrate EASEE's strengths against several real-world datasets, and its accuracy against known-answer synthetic datasets. Synthetic datasets' results show that (1) EASEE finds known-answer data shifts very quickly; and (2) ignoring these shifts drastically affects analytics on resulting snapshots. We show that previous work misses these shifts. Further, we evaluate EASEE against seven real-world datasets (330 K to 2.5B events), and find snapshot-over-time behaviors missed by previous works. Finally, we show that the resulting snapshots' measured properties (e.g., graph density) are altered by how snapshots are identified from the communication event stream. In particular, EASEE's snapshots do not generally “densify” over time, contradicting previous influential results that used simpler partitioning methods. 

Constant communities, i.e., groups of vertices that are always clustered together, independent of the community detection algorithm used, are necessary for reducing the inherent stochasticity of community detection results. Current methods for identifying constant communities require multiple runs of community detection algorithm(s). This process is extremely time consuming and not scalable to large networks. We propose a novel approach for finding the constant communities, by transforming the problem to a binary classification of edges. We apply the Otsu method from image thresholding to classify edges based on whether they are always within a community or not. Our algorithm does not require any explicit detection of communities and can thus scale to very large networks of the order of millions of vertices. Our results on real-world graphs show that our method is significantly faster and the constant communities produced have higher accuracy (as per F1 and NMI scores) than state-of-the-art baseline methods.