Scalable Approximate Biclique Counting over Large Bipartite Graphs

TL;DR

This paper introduces a scalable approximate method for counting $(p,q)$-bicliques in large bipartite graphs, using novel graph structures and sampling techniques to achieve high accuracy and efficiency.

Contribution

The authors propose a new $(p,q)$-broom structure and sampling algorithm that provide unbiased estimates with error guarantees for approximate biclique counting.

Findings

Outperforms existing methods in accuracy, reducing error by up to 8 times.

Achieves significant runtime speedup, up to 50 times faster.

Effective on nine real-world bipartite networks, demonstrating scalability.

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$\times$ error reduction) and runtime (up to 50$\times$ speedup) on nine real-world bipartite networks, providing a scalable solution for large-scale $(p,q)$-biclique counting.