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1. Belief Propagation with Quantum Messages for Symmetric Classical-Quantum Channels

   https://doi.org/10.1109/ITW54588.2022.9965841  

   Brandsen, S; Mandal, Avijit; Pfister, Henry D. (November 2022, 2022 IEEE Information Theory Workshop (ITW))

   Belief propagation (BP) is a classical algorithm that approximates the marginal distribution associated with a factor graph by passing messages between adjacent nodes in the graph. It gained popularity in the 1990’s as a powerful decoding algorithm for LDPC codes. In 2016, Renes introduced a belief propagation with quantum messages (BPQM) and described how it could be used to decode classical codes defined by tree factor graphs that are sent over the classical-quantum pure-state channel. In this work, we propose an extension of BPQM to general binary-input symmetric classical-quantum (BSCQ) channels based on the implementation of a symmetric "paired measurement". While this new paired-measurement BPQM (PMBPQM) approach is suboptimal in general, it provides a concrete BPQM decoder that can be implemented with local operations. Finally, we demonstrate that density evolution can be used to analyze the performance of PMBPQM on tree factor graphs. As an application, we compute noise thresholds of some LDPC codes with BPQM decoding for a class of BSCQ channels. 

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2. A performance predictor for implementation selection of parallelized static and temporal graph algorithms

   https://doi.org/10.1002/cpe.6267  

   Rehman, Akif; Ahmad, Masab; Khan, Omer (April 2021, Concurrency and Computation: Practice and Experience)

   Abstract Task‐based execution of graph workloads allows various ordered and unordered implementations, with tasks representing dependencies between graph vertices and edges. This work explores graph algorithms in the context of ordered and unordered task‐based implementations, that trade‐off work‐efficiency with parallelism. The monotonicity of convergent graph solutions is the reason behind the trade‐off between work‐efficiency and parallelism. This trade‐off results in variable performance‐based choices within and across different machines (CPUs and GPUs), graph algorithms, implementations (ordered, relaxed, and unordered). Input graphs also augment this choice space, with this work analyzing temporally changing graphs in addition to the static graphs explored by prior works. These algorithmic and architectural choices are first explored in this work, and it is seen that different graph workload‐input combinations perform optimally on diverse architectural configurations. The resulting choice space is analyzed and this work represents it in the form of characteristic variables that correlate with each choice space. Using these characteristic variables, this work proposes analytical and neural network models to correlate these choice spaces to find the best performing implementation. The variables and the prediction models proposed in this work are also integrated with a state‐of‐the‐art performance predictor on a multiaccelerator setup, and shows geometric performance gains of 54% on a CPU, 14% on a GPU, and 31.5% in a multiaccelerator setup over baseline implementations without performance prediction. 

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3. Direction-Optimizing Label Propagation Framework for Structure Detection in Graphs: Design, Implementation, and Experimental Analysis

   https://doi.org/10.1145/3564593  

   Liu, Xu T.; Lumsdaine, Andrew; Halappanavar, Mahantesh; Barker, Kevin; Gebremedhin, Assefaw H. (October 2022, ACM Journal of Experimental Algorithmics)

   Label Propagation is not only a well-known machine learning algorithm for classification, but it is also an effective method for discovering communities and connected components in networks. We propose a new Direction-Optimizing Label Propagation Algorithm (DOLPA) framework that enhances the performance of the standard Label Propagation Algorithm (LPA), increases its scalability, and extends its versatility and application scope. As a central feature, the DOLPA framework relies on the use of frontiers and alternates between label push and label pull operations to attain high performance. It is formulated in such a way that the same basic algorithm can be used for finding communities or connected components in graphs by only changing the objective function used. Additionally, DOLPA has parameters for tuning the processing order of vertices in a graph to reduce the number of edges visited and improve the quality of solution obtained. We present the design and implementation of the enhanced algorithm as well as our shared-memory parallelization of it using OpenMP. We also present an extensive experimental evaluation of our implementations using the LFR benchmark and real-world networks drawn from various domains. Compared with an implementation of LPA for community detection available in a widely used network analysis software, we achieve at most five times the F-Score while maintaining similar runtime for graphs with overlapping communities. We also compare DOLPA against an implementation of the Louvain method for community detection using the same LFR-graphs and show that DOLPA achieves about three times the F-Score at just 10% of the runtime. For connected component decomposition, our algorithm achieves orders of magnitude speedups over the basic LP-based algorithm on large diameter graphs, up to 13.2 × speedup over the Shiloach-Vishkin algorithm, and up to 1.6 × speedup over Afforest on an Intel Xeon processor using 40 threads. 

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4. Hyperbolic Graph Convolutional Neural Networks

   Chami, I.; Ying, R.; Ré, C.; Leskovec, J. (December 2019, Advances in neural information processing systems)

   Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative, as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges because it is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore, since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HGCN), the first inductive hyperbolic GCN that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive GCNs operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in hyperbolic spaces with different trainable curvature at each layer. Experiments demonstrate that HGCN learns embeddings that preserve hierarchical structure, and leads to improved performance when compared to Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GCNs, HGCN achieves an error reduction of up to 63.1% in ROC AUC for link prediction and of up to 47.5% in F1 score for node classification, also improving state-of-the art on the PubMed dataset. 

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5. Fast BFS-Based Triangle Counting on GPUs

   https://doi.org/10.1109/HPEC.2019.8916434  

   Wang, Leyuan; Owens, John D. (September 2019, Proceedings of the IEEE High Performance Extreme Computing Conference)

   In this paper, we propose a novel method, GSM, to compute graph matching (subgraph isomorphism) on GPUs. Unlike previous formulations of graph matching, our approach is BFS-based and thus can be mapped onto GPUs in a massively parallel fashion. Our implementation uses the Gunrock program- ming model and we evaluate our implementation in runtime and memory consumption compared with previous state-of-the- art work. We sustain a peak traversed-edges-per-second (TEPS) rate of nearly 10 GTEPS. Our algorithm is the most scalable and parallel among all existing GPU implementations and also outperforms all existing CPU distributed implementations. This work specifically focuses on leveraging our implementation on the triangle counting problem for the Subgraph Isomorphism Graph Challenge, demonstrating a geometric mean speedup over the 2018 champion of 3.84x 

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