A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Greedily finding a dense subgraph
Journal of Algorithms
Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
Approximation algorithms for maximization problems arising in graph partitioning
Journal of Algorithms
Complexity of finding dense subgraphs
Discrete Applied Mathematics
Massive Quasi-Clique Detection
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
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
Approximating Maximum Clique by Removing Subgraphs
SIAM Journal on Discrete Mathematics
Discovering large dense subgraphs in massive graphs
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Bioinformatics
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
On Effectively Finding Maximal Quasi-cliques in Graphs
Learning and Intelligent Optimization
Finding Dense Subgraphs with Size Bounds
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
Migration motif: a spatial - temporal pattern mining approach for financial markets
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
3-HOP: a high-compression indexing scheme for reachability query
Proceedings of the 2009 ACM SIGMOD International Conference on Management of data
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
An Efficient Algorithm for Solving Pseudo Clique Enumeration Problem
Algorithmica - Special Issue: Algorithms and Computation; Guest Editor: Takeshi Tokuyama
The community-search problem and how to plan a successful cocktail party
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Dense subgraph maintenance under streaming edge weight updates for real-time story identification
Proceedings of the VLDB Endowment
FENNEL: streaming graph partitioning for massive scale graphs
Proceedings of the 7th ACM international conference on Web search and data mining
Hi-index | 0.00 |
Finding dense subgraphs is an important graph-mining task with many applications. Given that the direct optimization of edge density is not meaningful, as even a single edge achieves maximum density, research has focused on optimizing alternative density functions. A very popular among such functions is the average degree, whose maximization leads to the well-known densest-subgraph notion. Surprisingly enough, however, densest subgraphs are typically large graphs, with small edge density and large diameter. In this paper, we define a novel density function, which gives subgraphs of much higher quality than densest subgraphs: the graphs found by our method are compact, dense, and with smaller diameter. We show that the proposed function can be derived from a general framework, which includes other important density functions as subcases and for which we show interesting general theoretical properties. To optimize the proposed function we provide an additive approximation algorithm and a local-search heuristic. Both algorithms are very efficient and scale well to large graphs. We evaluate our algorithms on real and synthetic datasets, and we also devise several application studies as variants of our original problem. When compared with the method that finds the subgraph of the largest average degree, our algorithms return denser subgraphs with smaller diameter. Finally, we discuss new interesting research directions that our problem leaves open.