Linear complexity SimRank computation based on the iterative diagonal estimation

TL;DR

This paper introduces a deterministic linear time algorithm for approximate SimRank computation with proven error bounds, leveraging iterative diagonal estimation to efficiently handle graph similarity queries.

Contribution

It proposes the IDE-SimRank method that estimates the diagonal matrix in the Lyapunov equation using GMRES, enabling fast approximate SimRank calculations.

Findings

Achieves linear time complexity for SimRank approximation

Provides error bounds for the approximate similarity scores

Efficiently handles single-source and pairwise similarity queries

Abstract

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.