MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY

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MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY ( models-and-algorithms-for-pagerank-sensitivity )

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Table 5.2 – Performance of the inner-outer iteration on various graphs. Total number of matrix- vector products and wall-clock time required for convergence to three different outer toler- ances τ, and the corresponding relative gains defined by (5.24). The parameters used here are α = 0.99, β = 0.5, η = 10−2 . For the first five graphs we used the Matlab mex codes, and for the final three large graphs we used the C++ codes where the graph is stored by out-edges and the times refer to the performance of an 8-core parallel code. 10−5 ubc-cs-2006 ubc 676 484 in-2004 657 428 eu-2005 499 476 wb-edu 647 417 arabic-2005 638 466 sk-2005 523 460 uk-2007 531 463 226 141 5.6 ⋅ numerical results 107 tol. graph work (mults.) power in/out time gain power 37.6% 1.9 41.7% 13.6 44.4% 51.1 -0.7% 26.9 41.2% 291.2 34.7% 779.2 7.7% 1718.2 13.8% 2802.0 24.7% 4.7 28.4% 37.7 34.9% 144.3 4.6% 89.3 35.5% 850.6 27.0% 2333.5 12.0% 5729.0 12.8% 10225.8 17.3% 8.0 23.6% 62.5 28.2% 243.1 9.2% 159.9 29.1% 1442.9 22.2% 3958.8 12.9% 10393.3 11.1% 18559.2 (secs.) in/out 1.2 8.3 30.4 28.3 184.6 502.5 1595.9 2359.3 3.6 27.8 97.5 87.4 572.0 1670.0 5077.1 8661.9 6.8 49.0 179.8 148.6 1059.0 3012.9 9122.9 16016.7 gain 35.2% 38.4% 40.5% -5.3% 36.6% 35.5% 7.1% 15.8% 22.9% 26.2% 32.4% 2.1% 32.8% 28.4% 11.4% 15.3% 15.4% 21.6% 26.0% 7.1% 26.6% 23.9% 12.2% 13.7% 10−3 ubc-cs-2006 ubc 242 141 in-2004 232 129 eu-2005 149 150 wb-edu 221 130 arabic-2005 213 139 sk-2005 156 144 uk-2007 145 125 574 432 10−7 ubc-cs-2006 ubc 1121 856 in-2004 1108 795 eu-2005 896 814 wb-edu 1096 777 arabic-2005 1083 843 sk-2005 951 828 uk-2007 964 857 986 815

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