HitSim: An Efficient Algorithm for Single-Source and Top-k SimRank Computation

Abstract SimRank is a widely-used metric for evaluating vertex similarity based on graph topology, with diverse applications such as large-scale graph mining and natural language processing. The objective of the single-source and top-k SimRank query problem is to retrieve the k vertices with the largest SimRank to the source vertex. However, existing algorithms suffer from inefficiency as they require computing SimRank for all vertices to retrieve the top-k results. To address this issue, we propose an algorithm named HitSim that utilizes a branch and bound strategy for the single-source and top-k query. HitSim initially partitions vertices into distinct sets based on their shortest-meeting lengths to the source vertex. Subsequently, it computes the upper bound of SimRank for each set. If the upper bound of a set is no larger than the minimum value of the current top-k results, HitSim efficiently batch prunes the unpromising vertices within the set. However, in scenarios where the graph becomes dense, certain sets with large upper bounds may contain numerous vertices with small SimRank, leading to redundant overhead when processing these vertices. To address this issue, we propose an optimized algorithm named HitSim-OPT that computes the upper bound of SimRank for each vertex instead of each set, resulting in a fine-grained and efficient pruning process. The experimental results conducted on six real-world datasets demonstrate the performance of our algorithms in efficiently addressing the single-source and top-k query problem.