Linear complexity SimRank computation based on the iterative diagonal estimation

This paper presents a deterministic linear time complexity IDE-SimRank method to approximately compute SimRank with proved error bound. SimRank is a well-known similarity measure between graph vertices which relies on graph topology only and is built on intuition that ”two objects are similar if they are related to similar objects”. The fixed point equation for direct SimRank computation is the discrete Lyapunov equation with specific diagonal matrix in the right hand side. The proposed method is based on estimation of this diagonal matrix with GMRES and use this estimation to compute singe-source and single pairs queries. These computations are executed with the part of series converging to the discrete Lyapunov equation solution.