1. PRSim: Sublinear Time SimRank Computation on Large Power-Law Graphs
Zhewei Wei, Xiaodong He, Xiaokui Xiao, Sibo Wang, Yu Liu, Xiaoyong Du, and Ji-Rong Wen
Contact:
Problems
Our Results:
Graph data
Assume a directed graph 𝐺=(𝑉,𝐸) with 𝑛 nodes and 𝑚 edges
SimRank:
Two objects are similar if they are referenced by similar objects, and
an object is most similar to itself.
High Level ideas:
𝑠(u,v) = 1 (1− 𝑐 ) 2 𝑙=0 ∞ 𝑤∈𝑉 𝜋 𝑙 (𝑢,𝑤) 𝜋 𝑙 (𝑣,𝑤)𝜂(𝑤)
Sort adj list according to in-degrees. Reversely sample backward walks
Backward Search on hub nodes (with large PageRanks) to build index
Applications
Web Mining [Jin01]
Social Network Analysis [Liben-Nowell07]
Spam Detection [Spirin11]
Objectives
Single-source query: Given a source node u, returns SimRank s(u,v) for every v
Top-k query: return v1,…,vk with highest SimRank
Allow an error of predetermined ε
Motivations
Experiments
Taxonomy
Datasets and methods:
Competitors: READS, SLING and TSF, the state-of-the-art index-based methods; ProbeSim and TopSim, the state-of-the-art index-free methods.
𝑐 -walk: at each step, terminates w.p. 1− 𝑐 , and move to a random in-neighbor w.p. 𝑐
SimRank s(u,v) = Pr[two 𝑐 -walks from u and v meet at the same step]
Experiments Results on Real-World Graphs
Outperforms competitors by at least one order of magnitudes
Sampling-based algorithm
Motivation 1: Linear Query Time
Sublinear query time is not possible on worst-case graphs
Can we achieve sub-linearity on real-world graphs?
Motivation 2: SimRank v.s. Graph structure
Performance of existing SimRank algorithms vary on graphs with similar number of nodes and edges
How does graph structure affect SimRank algorithms?
PRSim Algorithm
Experiments on Synthetic Graphs
All query costs reversely depend on power-law exponent 𝛾
Power-Law Graphs
Faction of nodes with
degree k: P 𝑘 ∼ 𝑘 −𝛾 ,
𝛾>𝟏
Codes: