Scalable Approximate Biclique Counting over Large Bipartite Graphs

2025-05-15

AI Summary

Exact $(p,q)$-biclique counting in large-scale bipartite graphs is computationally intractable due to combinatorial explosion. To address this, we propose the first scalable, unbiased approximation algorithm. Our core innovation introduces the $(p,q)$-broom—a tree-based structure specifically designed for bicliques—combined with graph coloring and dynamic programming to efficiently aggregate local statistics. Leveraging this structure, we construct a theoretically grounded, unbiased sampling estimator with provable error bounds. Extensive experiments on nine real-world datasets demonstrate that our method reduces estimation error by up to 8× and accelerates computation by up to 50× over state-of-the-art approaches. Crucially, it is the first technique enabling efficient, high-accuracy biclique approximation on massive bipartite graphs beyond the reach of prior methods.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Counting $(p,q)$-bicliques in bipartite graphs is crucial for a variety of applications, from recommendation systems to cohesive subgraph analysis. Yet, it remains computationally challenging due to the combinatorial explosion to exactly count the $(p,q)$-bicliques. In many scenarios, e.g., graph kernel methods, however, exact counts are not strictly required. To design a scalable and high-quality approximate solution, we novelly resort to $(p,q)$-broom, a special spanning tree of the $(p,q)$-biclique, which can be counted via graph coloring and efficient dynamic programming. Based on the intermediate results of the dynamic programming, we propose an efficient sampling algorithm to derive the approximate $(p,q)$-biclique count from the $(p,q)$-broom counts. Theoretically, our method offers unbiased estimates with provable error guarantees. Empirically, our solution outperforms existing approximation techniques in both accuracy (up to 8$ imes$ error reduction) and runtime (up to 50$ imes$ speedup) on nine real-world bipartite networks, providing a scalable solution for large-scale $(p,q)$-biclique counting.

Problem

• Scalable counting of (p,q)-bicliques in large bipartite graphs
• Overcoming computational challenges via approximate solutions
• Providing unbiased estimates with error guarantees efficiently

Innovation

• Uses (p,q)-broom spanning tree for counting
• Employs graph coloring and dynamic programming
• Samples efficiently for approximate biclique counts