Single-source and top-$k$ SimRank queries are two important types of similarity search in graphs with numerous applications in web mining, social network analysis, spam detection, etc. A plethora of techniques have been proposed for these two types of queries, but very few can efficiently support similarity search over large dynamic graphs, due to either significant preprocessing time or large space overheads. This paper presents ProbeSim, an index-free algorithm for single-source and top-$k$ SimRank queries that provides a non-trivial theoretical guarantee in the absolute error of query results. ProbeSim estimates SimRank similarities without precomputing any indexing structures, and thus can naturally support real-time SimRank queries on dynamic graphs. Besides the theoretical guarantee, ProbeSim also offers satisfying practical efficiency and effectiveness due to several non-trivial optimizations. We conduct extensive experiments on a number of benchmark datasets, which demonstrate that our solutions significantly outperform the existing methods in terms of efficiency and effectiveness. Notably, our experiments include the first empirical study that evaluates the effectiveness of SimRank algorithms on graphs with billion edges, using the idea of pooling.
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