Triangles are the basic substructure of networks and triangle counting (TC) has been a fundamental graph computing problem in numerous fields such as social network analysis. Nevertheless, like other graph computing problems, due to the high memory-computation ratio and random memory access pattern, TC involves a large amount of data transfers thus suffers from the bandwidth bottleneck in the traditional Von-Neumann architecture. To overcome this challenge, in this paper, we propose to accelerate TC with the emerging processing-in-memory (PIM) architecture through an algorithm-architecture co-optimization manner. To enable the efficient in-memory implementations, we come up to reformulate TC with bitwise logic operations (such as AND ), and develop customized graph compression and mapping techniques for efficient data flow management. With the emerging computational Spin-Transfer Torque Magnetic RAM (STT-MRAM) array, which is one of the most promising PIM enabling techniques, the device-to-architecture co-simulation results demonstrate that the proposed TC in-memory accelerator outperforms the state-of-the-art GPU and FPGA accelerations by $12.2\times$ and $31.8\times$ , respectively, and achieves a $34\times$ energy efficiency improvement over the FPGA accelerator.

Kernel ridge regression (KRR) is a powerful method for nonparametric regression. The time and space complexity of computing the KRR estimate directly are O(n ³ ) and O(n ² ), respectively, which are prohibitive for large-scale data sets, where n is the number of data. In this article, we propose a novel random sketch technique based on the circulant matrix that achieves savings in storage space and accelerates the solution of the KRR approximation. The circulant matrix has the following advantages: It can save time complexity by using the fast Fourier transform (FFT) to compute the product of matrix and vector, its space complexity is linear, and the circulant matrix, whose entries in the first column are independent of each other and obey the Gaussian distribution, is almost as effective as the i.i.d. Gaussian random matrix for approximating KRR. Combining the characteristics of the circulant matrix and our careful design, theoretical analysis and experimental results demonstrate that our proposed sketch method, making the estimate kernel methods scalable and practical for large-scale data problems, outperforms the state-of-the-art KRR estimates in time complexity while retaining similar accuracies. Meanwhile, our sketch method provides the theoretical bound that keeps the optimal convergence rate for approximating KRR.

Continual graph learning (CGL) is an important and challenging task that aims to extend static GNNs to dynamic task flow scenarios. As one of the mainstream CGL methods, the experience replay (ER) method receives widespread attention due to its superior performance. However, existing ER methods focus on identifying samples by feature significance or topological relevance, which limits their utilization of comprehensive graph data. In addition, the topology-based ER methods only consider local topological information and add neighboring nodes to the buffer, which ignores the global topological information and increases memory overhead. To bridge these gaps, we propose a novel method called Feature-Topology Fusion-based Experience Replay (FTF-ER) to effectively mitigate the catastrophic forgetting issue with enhanced efficiency. Specifically, from an overall perspective to maximize the utilization of the entire graph data, we propose a highly complementary approach including both feature and global topological information, which can significantly improve the effectiveness of the sampled nodes. Moreover, to further utilize global topological information, we propose Hodge Potential Score (HPS) as a novel module to calculate the topological importance of nodes. HPS derives a global node ranking via Hodge decomposition on graphs, providing more accurate global topological information compared to neighbor sampling. By excluding neighbor sampling, HPS significantly reduces buffer storage costs for acquiring topological information and simultaneously decreases training time. Compared with state-of-the-art methods, FTF-ER achieves a significant improvement of 3.6% in AA and 7.1% in AF on the OGB-Arxiv dataset, demonstrating its superior performance in the class-incremental learning setting.