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10 1 ⋅ introduction wb−edu, α = 0.85 0 10 0 10 −1 0 10 10 −1 wb−edu, α = 0.99 0 10 −2 10 −2 10 −3 10 −4 10 −5 10 −6 10 −7 10 10−2 10 10−2 −3 10 −4 10 −5 10 −6 10 −7 10 Residual Residual power inout power inout 10 20 30 40 50 60 70 80 Multiplication 200 400 600 800 1000 1200 Multiplication 5 101520 20 40 Figure1.4–PerformanceofthePageRankalgorithm. Theinner-outermethodclearlyoutper- forms the power method on wb-edu with α = 0.85 on the left and α = 0.99 on the right. The small inner figure shows the convergence in the first few iterations. See chapter 5 for details on the inner-outer method, and table 2.2 for information about the wb-edu graph. 1.5.1 Publications My original paper on the sensitivity analysis arising from the derivative of PageRank was written up in the proceedings from a Dagstuhl workshop [Gleich et al., 2007]. I still intend to submit these results to a journal, perhaps in combination with a few other ideas. A preliminary version of the random α PageRank idea was presented at the 2007 Workshop on Algorithms for the Web Graph [Constantine and Gleich, 2007]. We extended that manuscript to a journal-length article, which we plan to submit this summer. Although the inner-outer algorithm was originally proposed in [Gray et al., 2007], those authors graciously included my contributions into the current journal manuscript, which will be published in the SIAM Journal of Scientific Computing.9 9 A draft is available from www.cs. ubc.ca/~greif/Papers/gggl2009. pdf.PDF Image | Instagram Cheat Sheet
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