BIRD: Efficient Approximation of Bidirectional Hidden Personalized PageRank

In bipartite graph analysis, similarity measures play a pivotal role in various applications. Among existing metrics, the Bidirectional Hidden Personalized PageRank (BHPP) stands out for its superior query quality. However, the computational expense of BHPP remains a bottleneck. Existing approximation methods either demand significant matrix storage or incur prohibitive time costs. For example, current state-of-the-art methods require over 3 hours to process a single-source BHPP query on the real-world bipartite graph Orkut , which contains approximately 3 × 10 8 edges. We introduce BIRD, a novel algorithm designed for answering single-source BHPP queries on weighted bipartite graphs. Through meticulous theoretical analysis, we demonstrate that BIRD significantly improves time complexity to Õ ( n ), as compared to the previous best one, Õ ( m ), under typical relative error setting and constant failure probability. ( n, m denote the number of nodes and edges respectively.) Extensive experiments confirm that BIRD outperforms existing baselines by orders of magnitude in large-scale bipartite graphs. Notably, our proposed method accomplishes a single-source BHPP query on Orkut using merely 7 minutes.