Accuracy estimate and optimization techniques for SimRank computation

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.…”

“…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.…”

“…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.…”

“…To the best of our knowledge, there are several interesting pieces of work which can efficiently reduce the time complexity of SimRank deterministic computation. 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.…”

“…We first present a novel algorithm to estimate the SimRank between vertices in O n 3 + K · n 2 time, where n is the number of vertices, and K is the number of iterations. In comparison, the most efficient implementation of SimRank algorithm in [1] takes O K · n 3 time in the worst case. To efficiently handle large-scale computations, we also propose a parallel implementation of the SimRank algorithm on multiple processors.…”