A Local Algorithm for Finding Dense Bipartite-Like Subgraphs

  • Pan Peng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)


We give a local algorithm to extract dense bipartite-like subgraphs which characterize cyber-communities in the Web [13]. We use the bipartiteness ratio of a set as the quality measure that was introduced by Trevisan [20]. Our algorithm, denoted as FindDenseBipartite (v,s,θ), takes as input a starting vertex v, a volume target s and a bipartiteness ratio parameter θ and outputs an induced subgraph of G. It is guaranteed to have the following approximation performance: for any subgraph S with bipartiteness ratio θ, there exists a subset S θ  ⊆ S such that \(\textrm{vol}(S_\theta)\geq \textrm{vol}(S)/9\) and that if the starting vertex v ∈ S θ and \(s\geq \textrm{vol}(S)\), the algorithm FindDenseBipartite (v,s,θ) outputs a subgraph (X,Y) with bipartiteness ratio \(O(\sqrt{\theta})\). The running time of the algorithm is O(s 2(Δ + logs)), where Δ is the maximum degree of G, independent of the size of G.


Local Algorithm Laplacian Matrix Approximation Guarantee Sweep Process Spectral Algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pan Peng
    • 1
    • 2
  1. 1.State Key Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesP.R. China
  2. 2.School of Information Science and EngineeringGraduate University of China Academy of SciencesP.R. China

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