COCOON 2012: Computing and Combinatorics pp 145-156

# A Local Algorithm for Finding Dense Bipartite-Like Subgraphs

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

## Abstract

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.

## Keywords

Local Algorithm Laplacian Matrix Approximation Guarantee Sweep Process Spectral Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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