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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 Phi and volume k, a PageRank vector with a certain starting distribution can be used to produce a set with conductance (O(radic(Phi 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 oslash, whose small side has volume at least 2 ^b in time O(2 log m/(2 ^b log ² m/oslash ² ) where m is the number of edges in the graph. By combining small sets found by this local partitioning algorithm, we obtain a cut with conductance oslash and approximately optimal balance in time O(m log ⁴ m/oslash)","publishedDate","2006-01-01","publishedYear",2006,"venue","citationCount",981,"authors","keywords",[69,70,71],"pdfUrl","topVenue",false,"displayName","displayDescription","Algorithms and Data Compression","Complexity and Algorithms in Graphs","VLSI and FPGA Design 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Local Graph Partitioning using PageRank Vectors 论文

Local Graph Partitioning using PageRank Vectors · 相关文章