Subgraph matching has garnered increasing attention for its diverse real-world applications. Given the dynamic nature of real-world graphs, addressing evolving scenarios with-out incurring prohibitive overheads has been a focus of research. However, existing approaches for dynamic subgraph matching often proceed serially, retrieving incremental matches for each updated edge individually. This approach falls short when handling batch data updates, leading to a decrease in system throughput. Leveraging the parallel processing power of GPUs, which can execute a massive number of cores simultaneously, has been widely recognized for performance acceleration in various domains. Surprisingly, systematic exploration of subgraph matching in the context of batch-dynamic graphs, particularly on a GPU platform, remains untouched. In this paper, we bridge this gap by introducing an efficient framework, GAMMA (GPU-Accelerated Batch-Dynamic Subgraph Matching). Our approach features a DFS-based warp-centric batch-dynamic subgraph matching algorithm. To ensure load balance in the DFS-based search, we propose warp-level work stealing via shared memory. Additionally, we introduce coalesced search to reduce redundant computations. Comprehensive experiments demonstrate the superior performance of GAMMA. Compared to state-of-the-art algorithms, GAMMA showcases a performance improvement up to hundreds of times.

Counting ($p$, q)-bicliques in bipartite graphs poses a foundational challenge with broad applications, from densest sub-graph discovery in algorithmic research to personalized content recommendation in practical scenarios. Despite its significance, current leading ($p$, q)-biclique counting algorithms fall short, particularly when faced with larger graph sizes and clique scales. Fortunately, the problem's inherent structure, allowing for the independent counting of each biclique starting from every vertex, combined with a substantial set intersections, makes it highly amenable to parallelization. Recent successes in GPU-accelerated algorithms across various domains motivate our exploration into harnessing the parallelism power of GPUs to efficiently address the ($p$, q)-biclique counting challenge. We introduce GBC (GPU-based Biclique Counting), a novel approach designed to enable efficient and scalable ($p$, q)-biclique counting on GPUs. To address major bottleneck arising from redundant comparisons in set intersections (occupying an average of 90% of the runtime), we introduce a novel data structure that hashes adjacency lists into truncated bitmaps to enable efficient set intersection on GPUs via bit-wise AND operations. Our in-novative hybrid DFS-BFS exploration strategy further enhances thread utilization and effectively manages memory constraints. A composite load balancing strategy, integrating pre-runtime and runtime workload allocation, ensures equitable distribution among threads. Additionally, we employ vertex reordering and graph partitioning strategies for improved compactness and scalability. Experimental evaluations on eight real-life and two synthetic datasets demonstrate that GBC outperforms state-of-the-art algorithms by a substantial margin. In particular, GBC achieves an average speedup of$497.8\times$, with the largest instance achieving a remarkable$1217.7\times$speedup when$p=q=8$.

Graph pattern matching has been extensively investigated on general graphs without time information over decades. Nevertheless, few studies focus on temporal graphs, where a relationship between two vertices takes place at a specific moment and lingers for some time. In this paper, we propose a new notion so-calledtime-respecting flow graph, in which all paths are time-respecting (i.e., a sequence of contacts with non-decreasing time), and one vertex is distinguished as the root, from which other vertices can be reached via a time-respecting path. Based on this, we explore the problem oftime-respecting flow graph pattern matching on temporal graphs. This problem motivates important applications in epidemiology, information diffusion, crime detection, etc. To address it, we present one baseline algorithm as well as two optimized algorithms that utilize several efficient matching strategies and topological sort based technique to boost efficiency. Extensive experimental evaluation using both real and synthetic data sets demonstrates the effectiveness and efficiency of our proposed algorithms. Compared with baseline method, our optimized algorithms could achieve up to three orders of magnitude speedup.