A Space and Time Efficient Algorithm for SimRank Computation

Abstract

SimRank has become an important similarity measure to rank web documents based on a graph model on hyperlinks. The existing approaches for conducting SimRank computation adopt an iteration paradigm. The most efficient deterministic technique yieldsworst-case time per iteration with the space requirement O (, where n is the number of nodes (web documents). In this paper, we propose novel optimization techniques such that each iteration takes O (min {n · m, n r }) time and O (n + m) space, where m is the number of edges in a web-graph model and r ≤ log 2 7. In addition, we extend the similarity transition matrix to prevent random surfers getting stuck, and devise a pruning technique to eliminate impractical similarities for each iteration. Moreover, we also develop a reordering technique combined with an over-relaxation method, not only speeding up the convergence rate of the existing techniques, but achieving I/O efficiency as well. We conduct extensive experiments on both synthetic and real data sets to demonstrate the efficiency and effectiveness of our iteration techniques.

Taming Computational Complexity: Efficient and Parallel SimRank Optimizations on Undirected Graphs

“…In spite of the substantial improvement achieved by these existing techniques [1,7], high performance of SimRank computation involving fast algorithms and parallel implementation is still a challenging problem. However, the time requirements of the available SimRank deterministic algorithms are still about cubic in the number of vertices for each iteration, which is costly over large web graphs.…”

“…AUG-SimRank and PAUG-SimRank) on both synthetic and real data sets. We compare their performances with the most efficient existing algorithms proposed in [1] and [7]. The experiments were done on 2.0GHz Pentium(R) Dual-Core CPU with 2GB main memory, running Windows Vista OS.…”

“…Existing techniques for SimRank computation can be distinguished into two categories: (i) probabilistic method [3,4] that estimates SimRank by the expected value s (a, b) = E (c τ (a,b) ), where τ (a,b) is a random variable denoting the first meeting time for vertices a and b, and c ∈ (0, 1) is a decay factor; (ii) deterministic method [1,5,6,7] that computes SimRank iteratively for finding a fixed point of the SimRank function s (a, b). Since the latter approach produces better accuracy with high time complexity compared to the probabilistic method, there has been a growing interest in SimRank deterministic optimization over the recent years.…”

“…One work [1] is mainly based on a partial sums function reducing the computational time from O Kn 4 to O Kn 3 in the worst case. Another work [7] oriented on matrix representations takes O (K min (mn, n r )) time, where m is the number of edges, and r ∈ (2, log 2 7] is a positive constant. Li et al…”

“…It has been widely studied in the literature [2,3,4,1,5,6,7]. As a multi-step generalization of co-citation [8,9], SimRank similarity is based on the recursive concept that two different vertices are similar if their neighbors are similar.…”