A Local Algorithm for Finding Dense Subgraphs
<|reference_start|>A Local Algorithm for Finding Dense Subgraphs: 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.<|reference_end|>
@article{andersen2007a,
    title={A Local Algorithm for Finding Dense Subgraphs},
    author={Reid Andersen},
    journal={arXiv preprint arXiv:cs/0702078},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0702078},
    primaryClass={cs.DS cs.CC}
}