Finding good approximate vertex and edge partitions is NP-hard
Information Processing Letters
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
IEEE Transactions on Parallel and Distributed Systems
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Graph partitioning models for parallel computing
Parallel Computing - Special issue on graph partioning and parallel computing
Approximation Hardness of Bounded Degree MIN-CSP and MIN-BISECTION
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Sourcebook of parallel computing
Sourcebook of parallel computing
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A uniform approach to accelerated PageRank computation
WWW '05 Proceedings of the 14th international conference on World Wide Web
Learning from labeled and unlabeled data on a directed graph
ICML '05 Proceedings of the 22nd international conference on Machine learning
Additive Schwarz Iterations for Markov Chains
SIAM Journal on Matrix Analysis and Applications
Local Graph Partitioning using PageRank Vectors
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Weighted Graph Cuts without Eigenvectors A Multilevel Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
The VLDB Journal — The International Journal on Very Large Data Bases
A local algorithm for finding dense subgraphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Statistical properties of community structure in large social and information networks
Proceedings of the 17th international conference on World Wide Web
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Multi-assignment clustering for Boolean data
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Minimizing communication in sparse matrix solvers
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
A model of computation for MapReduce
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Advantage of overlapping clusters for minimizing conductance
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Distributed large-scale natural graph factorization
Proceedings of the 22nd international conference on World Wide Web
Fast iterative graph computation with block updates
Proceedings of the VLDB Endowment
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Most graph decomposition procedures seek to partition a graph into disjoint sets of vertices. Motivated by applications of clustering in distributed computation, we describe a graph decomposition algorithm for the paradigm where the partitions intersect. This algorithm covers the vertex set with a collection of overlapping clusters. Each vertex in the graph is well-contained within some cluster in the collection. We then describe a framework for distributed computation across a collection of overlapping clusters and describe how this framework can be used in various algorithms based on the graph diffusion process. In particular, we focus on two illustrative examples: (i) the simulation of a randomly walking particle and (ii) the solution of a linear system, e.g. PageRank. Our simulation results for these two cases show a significant reduction in swapping between clusters in a random walk, a significant decrease in communication volume during a linear system solve in a geometric mesh, and some ability to reduce the communication volume during a linear system solve in an information network.