Fast Approximate Graph Partitioning Algorithms
SIAM Journal on Computing
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
A polynomial-time tree decomposition to minimize congestion
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Graph partitioning using single commodity flows
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Local Graph Partitioning using PageRank Vectors
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Engineering graph clustering: Models and experimental evaluation
Journal of Experimental Algorithmics (JEA)
Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Multi-assignment clustering for Boolean data
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Overlapping clusters for distributed computation
Proceedings of the fifth ACM international conference on Web search and data mining
Finding overlapping communities in social networks: toward a rigorous approach
Proceedings of the 13th ACM Conference on Electronic Commerce
Overlapping community detection using seed set expansion
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
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Graph clustering is an important problem with applications to bioinformatics, community discovery in social networks, distributed computing, etc. While most of the research in this area has focused on clustering using disjoint clusters, many real datasets have inherently overlapping clusters. We compare overlapping and non-overlapping clusterings in graphs in the context of minimizing their conductance. It is known that allowing clusters to overlap gives better results in practice. We prove that overlapping clustering may be significantly better than non-overlapping clustering with respect to conductance, even in a theoretical setting. For minimizing the maximum conductance over the clusters, we give examples demonstrating that allowing overlaps can yield significantly better clusterings, namely, one that has much smaller optimum. In addition for the min-max variant, the overlapping version admits a simple approximation algorithm, while our algorithm for the non-overlapping version is complex and yields worse approximation ratio due to the presence of the additional constraint. Somewhat surprisingly, for the problem of minimizing the sum of conductances, we found out that allowing overlap does not really help. We show how to apply a general technique to transform any overlapping clustering into a non-overlapping one with only a modest increase in the sum of conductances. This uncrossing technique is of independent interest and may find further applications in the future.