Network proximity computations are among the most common operations in various data mining applications, including link prediction and collaborative filtering. A common measure of network proximity is Katz index, which has been shown to be among the best-performing path-based link prediction algorithms. With the emergence of very large network databases, such proximity computations become an important part of query processing in these databases. Consequently, significant effort has been devoted to developing algorithms for efficient computation of Katz index between a given pair of nodes or between a query node and every other node in the network. Here, we present LRC-Katz, an algorithm based on indexing and low rank correction to accelerate Katz index based network proximity queries. Using a variety of very large real-world networks, we show that LRC-Katzoutperforms the fastest existing method, Conjugate Gradient, for a wide range of parameter values. Taking advantage of the acceleration in the computation of Katz index, we propose a new link prediction algorithm that exploits locality of networks that are encountered in practical applications. Our experiments show that the resulting link prediction algorithm drastically outperforms state-of-the-art link prediction methods based on the vanilla and truncated Katz.