Comparison of Three Web Search Algorithms |
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Authors: | Ying Bao Zi-hu Zhu |
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Institution: | (1) Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China;(2) Graduate University of the Chinese Academy of Sciences, Beijing, 100049, China;(3) Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China |
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Abstract: | Abstract
In this paper we discuss three important kinds of Markov chains used in Web search algorithms-the maximal irreducible Markov
chain, the minimal irreducible Markov chain and the middle irreducible Markov chain. We discuss the stationary distributions,
the convergence rates and the Maclaurin series of the stationary distributions of the three kinds of Markov chains. Among
other things, our results show that the maximal and minimal Markov chains have the same stationary distribution and that the
stationary distribution of the middle Markov chain reflects the real Web structure more objectively. Our results also prove
that the maximal and middle Markov chains have the same convergence rate and that the maximal Markov chain converges faster
than the minimal Markov chain when the damping factor
.
Supported by the National Natural Science Foundation of China (No.10371034). |
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Keywords: | PageRank web search Markov chain stationary distribution convergence rate |
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