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Counting $(p,q)$-bicliques in bipartite graphs is crucial for a variety ofapplications, from recommendation systems to cohesive subgraph analysis. Yet,it remains computationally challenging due to the combinatorial explosion toexactly count the $(p,q)$-bicliques. In many scenarios, e.g., graph kernelmethods, however, exact counts are not strictly required. To design a scalableand high-quality approximate solution, we novelly resort to $(p,q)$-broom, aspecial spanning tree of the $(p,q)$-biclique, which can be counted via graphcoloring and efficient dynamic programming. Based on the intermediate resultsof the dynamic programming, we propose an efficient sampling algorithm toderive the approximate $(p,q)$-biclique count from the $(p,q)$-broom counts.Theoretically, our method offers unbiased estimates with provable errorguarantees. Empirically, our solution outperforms existing approximationtechniques in both accuracy (up to 8$\times$ error reduction) and runtime (upto 50$\times$ speedup) on nine real-world bipartite networks, providing ascalable solution for large-scale $(p,q)$-biclique counting.

Scalable Approximate Biclique Counting over Large Bipartite Graphs