SimRank is a classic measure of vertex-pair similarity according to the structure of graphs. Top- k and thresholding SimRank queries are two important types of similarity search with numerous applications in web mining, social network analysis, spam detection, etc. However, extensive studies for SimRank most focus on single-pair and single-source queries and fail to provide any feasible solution for the top- k and thresholding queries, e.g., with theoretical accuracy guarantee or acceptable empirical performance. In this paper, we propose SimTab (<u>Sim</u>Rank queries with <u>T</u>ighter confidence bounds and multi-<u>a</u>rmed <u>b</u>andits) to answer top- k and thresholding queries in a unified manner. First, we integrate several techniques with random walk sampling to tighten the confidence bound of SimRank estimation, which enhances the query efficiency. Second, we answer top- k and thresholding queries from the perspective of the Multi-Armed Bandits (MAB) problems. The proposed algorithms significantly improve the theoretical efficiency over state of the art, whereas the algorithmic complexity closely matches the hardness of the problem. We further propose a novel sampling strategy specially tailored for node similarity queries, which improves both the theoretical and practical query efficiency of the MAB-based algorithms. Our method is the first with query accuracy guarantee for these two queries, and the sole algorithm to achieve high-quality query results on large graphs. Moreover, all proposed algorithms are index-free, and thus can be naturally applied to dynamic graphs. Extensive experiments on several large graph datasets demonstrate that our algorithms achieve much superior effectiveness with comparable or less query time cost than all index-free and index-based state of the art. Besides, our work proposes the first thorough empirical evaluation of the existing SimRank algorithms over top- k and thresholding queries.

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