Edge-based Local Push for Personalized PageRank

Personalized PageRank (PPR) is a popular node proximity metric in graph mining and network research. A single-source PPR (SSPPR) query asks for the PPR value of each node on the graph. Due to its importance and wide applications, decades of efforts have been devoted to the efficient processing of SSPPR queries. Among existing algorithms, LocalPush is a fundamental method for SSPPR queries and serves as a cornerstone for subsequent algorithms. In LocalPush, a push operation is a crucial primitive operation, which distributes the probability at a node u to ALL u's neighbors via the corresponding edges. Although this push operation works well on unweighted graphs, unfortunately, it can be rather inefficient on weighted graphs. In particular, on unbalanced weighted graphs where only a few of these edges take the majority of the total weight among them, the push operation would have to distribute "insignificant" probabilities along those edges which just take the minor weights, resulting in expensive overhead. To resolve this issue, in this paper, we propose the EdgePush algorithm, a novel method for computing SSPPR queries on weighted graphs. EdgePush decomposes the aforementioned push operations in edge-based push, allowing the algorithm to operate at the edge level granularity. As a result, it can flexibly distribute the probabilities according to edge weights. Furthermore, our EdgePush allows a fine-grained termination threshold for each individual edge, leading to a superior complexity over LocalPush. Notably, we prove that EdgePush improves the theoretical query cost of LocalPush by an order of up to O(n) when the graph's weights are unbalanced. Our experimental results demonstrate that EdgePush significantly outperforms state-of-the-art baselines in terms of query efficiency on large motif-based and real-world weighted graphs.