Fast and Exact Top-k Search for Random Walk with Restart

Graphs are fundamental data structures and have been em-ployed for centuries to model real-world systems and phe-nomena. Random walk with restart (RWR) provides a goodproximity score between two nodes in a graph, and it hasbeen successfully used in many applications such as auto-matic image captioning, recommender systems, and link pre-diction. The goal of this work is to find nodes that have top-k highest proximities for a given node. Previous approachesto this problem find nodes efficiently at the expense of exact-ness. The main motivation of this paper is to answer, in theaffirmative, the question, ‘Is it possible to improve the searchtime without sacrificing the exactness?’. Our solution, K-dash, is based on two ideas: (1) It computes the proximityof a selected node efficiently by sparse matrices, and (2) Itskips unnecessary proximity computations when searchingfor the top-k nodes. Theoretical analyses show that K-dashguarantees result exactness. We perform comprehensive ex-periments to verify the efficiency of K-dash. The resultsshow that K-dash can find top-k nodes significantly fasterthan the previous approaches while it guarantees exactness.