Using PageRank to Locally Partition a Graph

13 years 4 months ago

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A local graph partitioning algorithm ﬁnds a cut near a speciﬁed starting vertex, with a running time that depends largely on the size of the small side of the cut, rather than the size of the input graph. In this paper, we present a local partitioning algorithm using a variation of PageRank with a speciﬁed starting distribution. We derive a mixing result for PageRank vectors similar to that for random walks, and show that the ordering of the vertices produced by a PageRank vector reveals a cut with small conductance. In particular, we show that for any set C with conductance Φ and volume k, a PageRank vector with a certain starting distribution can be used to produce a set with conductance O( √ Φ log k). We present an improved algorithm for computing approximate PageRank vectors, which allows us to ﬁnd such a set in time proportional to its size. In particular, we can ﬁnd a cut with conductance at most φ, whose small side has volume at least 2b , in time O(2b log2 m/φ2...

Reid Andersen, Fan R. K. Chung, Kevin J. Lang

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