Some Recent Results on Ranking Webpages and Websites

In this paper we briefly review some of our recent results on the research of the design and analysis of search engine algorithms. The contents include: the limiting behavior of PageRank when the damping factor tends to 1; comparison of the convergence rate of maximal and minimal irreducible Markov chains on the Internet; a new proposal of N -step PageRank algorithm; a new proposal of ranking Websites– AggregateRank Algorithm. As is well known that in recent years Web search engines have been more and more important in modern science and technology, and more and more popular in civil daily life. The design of Web search engines has been becoming a focus of the research on the Web search and mining. One popular aspect is to calculate Static Rank by exploiting the hyperlink structure of the Web. Researchers have made great progress on link analysis models and algorithms since 1998, such as HITS and PageRank ([9, 17]). In nowadays, PageRank has emerged a popular link ∗1Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China; 2Graduate University of the Chinese Academy of Sciences; 3School of Sciences, Beijing Jiaotong University, Beijing 100044, China (Email: [email protected], [email protected], [email protected]).