Maximal biclique enumeration (MBE) in bipartite graphs is an important problem in data mining with many real-world applications. Parallel MBE algorithms for GPUs are needed for MBE acceleration leveraging its many computing cores. However, enumerating maximal bicliques using GPUs has three main challenges including large memory requirement, thread divergence, and load imbalance. In this paper, we propose GMBE+, an advanced GPU solution for the MBE problem. To overcome the challenges, we design (1) a node-reuse approach to reduce GPU memory usage with advanced node pruning, (2) a bitmap-based set intersection approach to minimize thread divergence, and (3) a load-aware task scheduling framework to achieve load balance among threads within GPU warps, facilitated by a novel set union approach. Our experiments reveal that GMBE+ is 1.2× faster than the latest GPU-based MBE algorithm GMBE on average when running on the same NVIDIA A100 GPU.

Maximal biclique enumeration (MBE) is crucial in bipartite graph analysis. Recent studies rely on extensive set intersections on static bipartite graphs to solve the MBE problem. However, the computational subgraphs dynamically change during enumeration, leading to redundant memory accesses and degraded set intersection performance. To overcome this limitation, we propose an AdaMBE algorithm. First, we redesign its core operations using local neighborhood information derived from computational subgraphs to minimize redundant memory accesses. Second, we dynamically create computational subgraphs using bitmaps leveraging its fast bitwise operations to accelerate set intersections. Finally, we integrate them in AdaMBE. Our experimental results show that AdaMBE is $1.6 \times-49.7 \times$ faster than its closest CPU-based competitor and successfully enumerates all 19 billion maximal bicliques on the TVTropes dataset, a large task beyond the capabilities of existing algorithms. Notably, on certain datasets, our parallel version, ParAdaMBE, on CPUs even outperforms GMBE on GPUs by up to $5.07 \times$.

Maximal biclique enumeration (MBE) in bipartite graphs is a fundamental problem in data mining with widespread applications. Many recent works solve this problem based on the set-enumeration (SE) tree, which sequentially traverses vertices to generate the enumeration tree nodes representing distinct bicliques, then checks whether these bicliques are maximal or not. However, existing MBE algorithms only expand bicliques with untraversed vertices to ensure distinction, which often necessitate extensive node checks to eliminate non-maximal bicliques, resulting in significant computational overhead during the enumeration process. To address this issue, we propose an aggressive set-enumeration (ASE) tree that aggressively expands all bicliques to their maximal form, thus avoiding costly node checks on non-maximal bicliques. This aggressive enumeration may produce multiple duplicate maximal bicliques, but we efficiently eliminate these duplicates by leveraging the connection between parent and child nodes and conducting low-cost node checking. Additionally, we introduce an aggressive merge-based pruning (AMP) approach that aggressively merges vertices sharing the same local neighbors. This helps prune numerous duplicate node generations caused by subsets of merged vertices. We integrate the AMP approach into the ASE tree, and present the Aggressive Maximal Biclique Enumeration Algorithm (AMBEA). Experimental results show that AMBEA is 1.15$\times$to 5.32$\times$faster than its closest competitor and exhibits better scalability and parallelization capabilities on larger bipartite graphs.

Maximal biclique enumeration (MBE) in bipartite graphs is an important problem in data mining with many real-world applications. All existing solutions for MBE are designed for CPUs. Parallel MBE algorithms for GPUs are needed for MBE acceleration leveraging its many computing cores. However, enumerating maximal bicliques using GPUs has three main challenges including large memory requirement, thread divergence, and load imbalance. In this paper, we propose GMBE, the first highly-efficient GPU solution for the MBE problem. To overcome the challenges, we design a node-reuse approach to reduce GPU memory usage, a pro-active pruning method using the vertex's local neighborhood size to alleviate thread divergence, and a load-aware task scheduling framework to achieve load balance among threads within GPU warps and blocks. Our experimental results show that GMBE on an NVIDIA A100 GPU can achieve 70.6× speedup over the state-of-the-art parallel MBE algorithm ParMBE on a 96-core CPU machine.