A Local Algorithm for Finding Dense Subgraphs

Details A Local Algorithm for Finding Dense Subgraphs A Local Algorithm for Finding Dense Subgraphs

2007-02-13

arxiv.org/abs/cs/0702078v1

Computer Science

Data Structures and Algorithms

14 pages, no figures

Scientific paper

We present a local algorithm for finding dense subgraphs of bipartite graphs, according to the definition of density proposed by Kannan and Vinay. Our algorithm takes as input a bipartite graph with a specified starting vertex, and attempts to find a dense subgraph near that vertex. We prove that for any subgraph S with k vertices and density theta, there are a significant number of starting vertices within S for which our algorithm produces a subgraph S' with density theta / O(log n) on at most O(D k^2) vertices, where D is the maximum degree. The running time of the algorithm is O(D k^2), independent of the number of vertices in the graph.

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