Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Efficient identification of Web communities
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
Introduction to Algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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
0(\sqrt {\log n)} Approximation to SPARSEST CUT in Õ(n2) Time
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Graph partitioning using single commodity flows
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Statistical properties of community structure in large social and information networks
Proceedings of the 17th international conference on World Wide Web
On partitioning graphs via single commodity flows
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Conductance and convergence of Markov chains-a combinatorial treatment of expanders
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
The simple random walk and max-degree walk on a directed graph
Random Structures & Algorithms
Spectral Sparsification of Graphs
SIAM Journal on Computing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The laplacian paradigm: emerging algorithms for massive graphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Streaming graph partitioning for large distributed graphs
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
The small community phenomenon in networks: models, algorithms and applications
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Algorithms, graph theory, and the solution of laplacian linear equations
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Spectral sparsification of graphs: theory and algorithms
Communications of the ACM
Fast image/video collection summarization with local clustering
Proceedings of the 21st ACM international conference on Multimedia
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A local graph partitioning algorithm finds a set of vertices with small conductance (i.e.~a sparse cut) by adaptively exploring a large graph G, starting from a specified vertex. For the algorithm to be local, its complexity must be bounded in terms of the size of the set it outputs, with at most a weak dependence on n, the number of vertices in G. Previous local partitioning algorithms find sparse cuts using random walks and personalized PageRank. In this paper, we introduce a randomized local partitioning algorithm that finds a sparse cut by simulating the volume-biased evolving set process, which is a Markov chain on sets of vertices. We prove that for any set of vertices A that has conductance at most φ, and for at least half of the starting vertices in A, our algorithm will output (with probability at least half) a set of conductance O(φ1/2 log1/2 n). The complexity of a local partitioning algorithm is measured by its work/volume ratio, which is the ratio between the computational complexity of the algorithm on a given run, and the volume of the set output. We prove that for our algorithm, the expected value of the work/volume ratio is polylognoparen(φ-1/2). The best previous local partitioning algorithm, due to Andersen, Chung, and Lang, has the same approximation guarantee but a larger work/volume ratio of polylognoparen(φ-1). As an application of our local partitioning algorithm, we construct a fast algorithm for finding balanced cuts. The resulting algorithm takes as input a graph and a fixed value of φ, has complexity polylog{m+nφ-1/2), and returns a cut with conductance O(φ1/2 log1/2 n) and volume at least vφ/2, where vφ is the volume of the largest set in the graph with conductance at most φ.