A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Journal of Algorithms
SIAM Journal on Computing
Trawling the Web for emerging cyber-communities
WWW '99 Proceedings of the eighth international conference on World Wide Web
Finding a Maximum Density Subgraph
Finding a Maximum Density Subgraph
On the densest k-subgraph problems
On the densest k-subgraph problems
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Constructing Expander Graphs by 2-Lifts and Discrepancy vs. Spectral Gap
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Discovering large dense subgraphs in massive graphs
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Local Graph Partitioning using PageRank Vectors
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Finding Dense Subgraphs with Size Bounds
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
A local algorithm for finding dense subgraphs
ACM Transactions on Algorithms (TALG)
Extracting local community structure from local cores
DASFAA'11 Proceedings of the 16th international conference on Database systems for advanced applications
Improving video classification via youtube video co-watch data
SBNMA '11 Proceedings of the 2011 ACM workshop on Social and behavioural networked media access
Overlapping clusters for distributed computation
Proceedings of the fifth ACM international conference on Web search and data mining
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A local graph algorithm is one that searches for an approximation of the best solution near a specified starting vertex, and has a running time independent of the size of the graph. Recently, local algorithms have been developed for graph partitioning and clustering. In this paper, we present a local algorithm for finding dense subgraphs of bipartite graphs, according to the measure of density proposed by Kannan and Vinay. The algorithm takes as input a bipartite graph with a specified starting vertex, and attempts to find a dense subgraph near that vertex. We prove the following local approximation guarantee for the algorithm. For any subgraph S with k vertices and density θ, there is a large set of starting vertices within S for which the algorithm produces a subgraph with density Ω(θ/log Δ), where Δ is the maximum degree. The running time of the algorithm is O(Δk2), independent of the number of vertices in the graph.