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
Greedy approximation algorithms for finding dense components in a graph
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
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
A local algorithm for finding dense subgraphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Finding Dense Subgraphs with Size Bounds
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
Extracting local community structure from local cores
DASFAA'11 Proceedings of the 16th international conference on Database systems for advanced applications
| Hi-index | 0.00 |
We describe a local algorithm for finding subgraphs with high density, according to a measure of density introduced by Kannan and Vinay [1999]. The algorithm takes as input a bipartite graph G, a starting vertex v, and a parameter k, and outputs an induced subgraph of G. It is local in the sense that it does not examine the entire input graph; instead, it adaptively explores a region of the graph near the starting vertex. The running time of the algorithm is bounded by O(Δ k2), which depends on the maximum degree Δ, but is otherwise independent of the graph. We prove the following approximation guarantee: for any subgraph S with k′ vertices and density θ, there exists a set S′ ⊆ S for which the algorithm outputs a subgraph with density Ω(θ/log Δ) whenever v ∈ S′ and k ≥ k′. We prove that S′ contains at least half of the edges in S.