A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Authoritative sources in a hyperlinked environment
Journal of the ACM (JACM)
Complexity of finding dense subgraphs
Discrete Applied Mathematics
Greedily Finding a Dense Subgraph
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
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
Discovering large dense subgraphs in massive graphs
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Extraction and classification of dense communities in the web
Proceedings of the 16th international conference on World Wide Web
Ruling Out PTAS for Graph Min-Bisection, Dense k-Subgraph, and Bipartite Clique
SIAM Journal on Computing
A scalable pattern mining approach to web graph compression with communities
WSDM '08 Proceedings of the 2008 International Conference on Web Search and Data Mining
Finding Dense Subgraphs with Size Bounds
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Densest k-subgraph approximation on intersection graphs
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Mining social networks and their visual semantics from social photos
Proceedings of the International Conference on Web Intelligence, Mining and Semantics
Link prediction for annotation graphs using graph summarization
ISWC'11 Proceedings of the 10th international conference on The semantic web - Volume Part I
An OpenMP algorithm and implementation for clustering biological graphs
Proceedings of the first workshop on Irregular applications: architectures and algorithm
Densest subgraph in streaming and MapReduce
Proceedings of the VLDB Endowment
Dense subgraphs with restrictions and applications to gene annotation graphs
RECOMB'10 Proceedings of the 14th Annual international conference on Research in Computational Molecular Biology
Dense subgraph maintenance under streaming edge weight updates for real-time story identification
Proceedings of the VLDB Endowment
Managing large dynamic graphs efficiently
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Brief announcement: maintaining large dense subgraphs on dynamic networks
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Finding cross genome patterns in annotation graphs
DILS'12 Proceedings of the 8th international conference on Data Integration in the Life Sciences
Finding dense subgraphs of sparse graphs
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Dense subgraphs on dynamic networks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Denser than the densest subgraph: extracting optimal quasi-cliques with quality guarantees
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Towards realistic team formation in social networks based on densest subgraphs
Proceedings of the 22nd international conference on World Wide Web
Truncated power method for sparse eigenvalue problems
The Journal of Machine Learning Research
Permutation indexing: fast approximate retrieval from large corpora
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
SQBC: An efficient subgraph matching method over large and dense graphs
Information Sciences: an International Journal
Exploiting small world property for network clustering
World Wide Web
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Given an undirected graph G = (V ,E ), the density of a subgraph on vertex set S is defined as $d(S)=\frac{|E(S)|}{|S|}$, where E (S ) is the set of edges in the subgraph induced by nodes in S . Finding subgraphs of maximum density is a very well studied problem. One can also generalize this notion to directed graphs. For a directed graph one notion of density given by Kannan and Vinay [12] is as follows: given subsets S and T of vertices, the density of the subgraph is $d(S,T)=\frac{|E(S,T)|}{\sqrt{|S||T|}}$, where E (S ,T ) is the set of edges going from S to T . Without any size constraints, a subgraph of maximum density can be found in polynomial time. When we require the subgraph to have a specified size, the problem of finding a maximum density subgraph becomes NP -hard. In this paper we focus on developing fast polynomial time algorithms for several variations of dense subgraph problems for both directed and undirected graphs. When there is no size bound, we extend the flow based technique for obtaining a densest subgraph in directed graphs and also give a linear time 2-approximation algorithm for it. When a size lower bound is specified for both directed and undirected cases, we show that the problem is NP-complete and give fast algorithms to find subgraphs within a factor 2 of the optimum density. We also show that solving the densest subgraph problem with an upper bound on size is as hard as solving the problem with an exact size constraint, within a constant factor.