Multi-core & GPU-based Balanced Butterfly Counting in Signed Bipartite Graphs

TL;DR

This work tackles scalable balanced butterfly counting in signed bipartite graphs, a fundamental primitive for understanding local balance and higher-order motifs in signed networks. It introduces a multi-core CPU method (M-BBC) and two GPU methods (G-BBC, G-BBC++) built on tile-based shared-memory processing and dynamic load balancing, extending prior unsigned-bipartite approaches to the signed setting. Extensive experiments on 15 real datasets show substantial performance gains over a serial baseline (BB2K) and its CPU counterpart (SBCList++), with GPU methods achieving up to 13,230x speedups and GPU-based variants averaging around 2,599x over BB2K and 50x over M-BBC. The results demonstrate the practicality of high-performance signed motif analysis at scale and lay a foundation for broader motif mining in signed bipartite networks.

Abstract

Balanced butterfly counting, corresponding to counting balanced (2, 2)-bicliques, is a fundamental primitive in the analysis of signed bipartite graphs and provides a basis for studying higher-order structural properties such as clustering coefficients and community structure. Although prior work has proposed an efficient CPU-based serial method for counting balanced (2, k)-bicliques. The computational cost of balanced butterfly counting remains a major bottleneck on large-scale graphs. In this work, we present the highly parallel implementations for balanced butterfly counting for both multicore CPUs and GPUs. The proposed multi-core algorithm (M-BBC) employs fine-grained vertex-level parallelism to accelerate wedge-based counting while eliminating the generation of unbalanced substructures. To improve scalability, we develop a GPU-based method (G-BBC) that uses a tile-based parallel approach to effectively leverage shared memory while handling large vertex sets. We then present an improved variation, G-BBC++, which integrates dynamic scheduling to mitigate workload imbalance and maximize throughput. We conduct an experimental assessment of the proposed methods across 15 real-world datasets. Experimental results exhibit that M-BBC achieves speedups of up to 71.13x (average 38.13x) over the sequential baseline BB2K. The GPU-based algorithms deliver even greater improvements, achieving up to 13,320x speedup (average 2,600x) over BB2K and outperforming M-BBC by up to 186x (average 50x). These results indicate the substantial scalability and efficiency of our parallel algorithms and establish a robust foundation for high-performance signed motif analysis on massive bipartite graphs.

Figures (13)

• Figure 1: Example of (a) a bipartite graph (gray lines denote edges) and (b) a signed bipartite graph (solid/dashed edges denote positive/negative edges, respectively).
• Figure 2: An illustration of balanced and unbalanced butterflies.
• Figure 3: A wedge in an unsigned bipartite graph.
• Figure 4: Symmetric wedges (a) and (b) in a signed bipartite graph.
• Figure 5: Asymmetric wedge in a signed bipartite graph.

Theorems & Definitions (11)

• Definition 1: Butterfly wang2019vertex
• Definition 2: Balanced Butterfly derr2019balance
• Definition 3: Biclique derr2019balance
• Definition 4: Balanced Signed biclique
• Definition 5: Balanced $(2,k)$-Biclique
• Definition 6: Vertex Priority wang2019vertex
• Definition 7: Wedge ($\lor$) wang2019vertex
• Definition 8: Symmetric Wedge ($\lor^s$) kiran2024efficient
• Definition 9: Asymmetric Wedge ($\lor^a$) kiran2024efficient
• Lemma 1