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WWW '03 Proceedings of the 12th international conference on World Wide Web
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Hardness of cut problems in directed graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
To randomize or not to randomize: space optimal summaries for hyperlink analysis
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
Conductance and convergence of Markov chains-a combinatorial treatment of expanders
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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Proceedings of the 31st annual international ACM SIGIR conference on Research and development in information retrieval
Symmetrizations for clustering directed graphs
Proceedings of the 14th International Conference on Extending Database Technology
Multi-commodity allocation for dynamic demands using pagerank vectors
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
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A local partitioning algorithm finds a set with small conductance near a specified seed vertex. In this paper, we present a generalization of a local partitioning algorithm for undirected graphs to strongly connected directed graphs. In particular, we prove that by computing a personalized PageRank vector in a directed graph, starting from a single seed vertex within a set S that has conductance at most α, and by performing a sweep over that vector, we can obtain a set of vertices S′ with conductance ΦM(S′) = O(√α log |S|). Here, the conductance function ΦM is defined in terms of the stationary distribution of a random walk in the directed graph. In addition, we describe how this algorithm may be applied to the PageRank Markov chain of an arbitrary directed graph, which provides a way to partition directed graphs that are not strongly connected.