A Space and Time Efficient Algorithm for SimRank Computation

Abstract

SimRank has been proposed to rank web documents based on a graph model on hyperlinks. The existing techniques for conducting SimRank computation adopt an iteration computation paradigm. The most efficient technique has the time complexity O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) with the space requirement O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) in the worst case for each iteration where n is the number of nodes (web documents). In this paper, we propose novel optimization techniques such that each iteration takes the time O(min{n · m,n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> }) and requires space O (n + m) where m is the number of edges in a web-graph model and r ≤ log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> 7. We also show that our algorithm accelerates the convergence rate of the existing techniques. Moreover, our algorithm not only reduces the time and space complexity of the existing techniques but is also I/O efficient. We conduct extensive experiments on both synthetic and real data sets to demonstrate the efficiency and effectiveness of our iteration techniques.