Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
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Journal of the ACM (JACM)
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Efficient identification of Web communities
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
Algorithms for graph partitioning on the planted partition model
Random Structures & Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A practical algorithm for constructing oblivious routing schemes
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
A polynomial-time tree decomposition to minimize congestion
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
On clusterings: Good, bad and spectral
Journal of the ACM (JACM)
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
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Proceedings of the 15th international conference on World Wide Web
Local Graph Partitioning using PageRank Vectors
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
Empirical comparison of algorithms for network community detection
Proceedings of the 19th international conference on World wide web
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
SHRINK: a structural clustering algorithm for detecting hierarchical communities in networks
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
On the NP-Completeness of some graph cluster measures
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Finding overlapping communities in social networks: toward a rigorous approach
Proceedings of the 13th ACM Conference on Electronic Commerce
Computer Science Review
Beyond Social Graphs: User Interactions in Online Social Networks and their Implications
ACM Transactions on the Web (TWEB)
Modeling and detecting community hierarchies
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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The detection of communities in real-world large-scale complex networks is a fundamental step in many applications, such as describing community structure and predicting the dissemination of information. Unfortunately, community detection is a computationally expensive task. Indeed, many approaches with strong theoretic guarantees are infeasible when applied to networks of large scale. Numerous approaches have been designed to scale community detection algorithms, many of which leverage local optimizations or local greedy decisions to iteratively find the communities. Solely relying on local techniques to detect communities, rather than a global objective function, can fail to detect global structure of the network. In this work, we instead formulate a notion of a hierarchical community decomposition (HCD), which takes a more global view of hierarchical community structure. Our main contributions are as follows. We formally define a (λ, delta)-HCD where λ parametrizes the connectivity within each sub-community at the same hierarchical level and δ parametrizes the relationship between communities across two consecutive levels. Based on a method of Racke originally designed for oblivious routing, we provide an algorithm to construct a HCD and prove that an (O(log n);O(1))-HCD can always be found for any n-node input graph. Further, our algorithm does not rely on a pre-specified number of communities or depth of decomposition. Since the algorithm is of exponential complexity, we also describe a practical efficient, yet heuristic, implementation and perform an experimental validation on synthetic and real-world networks. We experiment first with synthetic networks with well-defined "intended" decompositions, on which we verify the quality of the decompositions produced by our method. Armed with the confidence these positive results provide, we use our implementation to compute the hierarchical community structure of more complex, real-world networks.