ASAP: towards accurate, stable and accelerative penetrating-rank estimation on large graphs

  • Authors:

  • Xuefei Li;Weiren Yu;Bo Yang;Jiajin Le

  • Affiliations:

  • Fudan University, China;University of New South Wales & NICTA, Australia and Donghua University, China;Donghua University, China;Donghua University, China

  • Venue:
  • WAIM'11 Proceedings of the 12th international conference on Web-age information management
  • Year:
  • 2011

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Abstract

Pervasive web applications increasingly require a measure of similarity among objects. Penetrating-Rank (P-Rank) has been one of the promising link-based similarity metrics as it provides a comprehensive way of jointly encoding both incoming and outgoing links into computation for emerging applications. In this paper, we investigate P-Rank efficiency problem that encompasses its accuracy, stability and computational time. (1)We provide an accuracy estimate for iteratively computing P-Rank. A symmetric problem is to find the iteration number K needed for achieving a given accuracy ε. (2) We also analyze the stability of P-Rank, by showing that small choices of the damping factors would make P-Rank more stable and well-conditioned. (3) For undirected graphs, we also explicitly characterize the P-Rank solution in terms of matrices. This results in a novel non-iterative algorithm, termed ASAP, for efficiently computing P-Rank, which improves the CPU time from O(n4) to O(n3). Using real and synthetic data, we empirically verify the effectiveness and efficiency of our approaches.