An algebraic multigrid solution of large hierarchical Markovian models arising in web information retrieval

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5233, Issue , 2011, Pages 548-570

  Krieger, Udo R ^a  

^a UNIVERSITY OF BAMBERG   (Germany)

Author keywords

algebraic multigrid; Markov chain; page rank; Web information retrieval

Indexed keywords

ALGEBRA; HIERARCHICAL CLUSTERING; ITERATIVE METHODS; MARKOV CHAINS; STOCHASTIC SYSTEMS;

AGGREGATION/DISAGGREGATION; ALGEBRAIC MULTIGRID METHODS; ALGEBRAIC MULTIGRIDS; HIERARCHICAL MARKOVIAN MODELS; HOMOGENEOUS MARKOV CHAINS; PAGE RANKS; STATIONARY DISTRIBUTION; WEB INFORMATION RETRIEVAL;

INFORMATION RETRIEVAL;

EID: 79955822464     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02742-0_23     Document Type: Article

References (24)

1. Baldi, P., et al.: Modeling the Internet and the Web - Probabilistic Methods and Algorithms. John Wiley & Sons, Chichester (2003)
2. Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York (1979)
3. Cao, W., Stewart, W.J.: Iterative aggregation/disaggregation techniques for nearly uncoupled Markov chains. Journal of the ACM 32, 702-719 (1985) (Pubitemid 15507397)
4. Chatelin, F., Miranker, W.L.: Acceleration by aggregation of successive approximation methods. Linear Algebra and its Applications 43, 17-47 (1982)
5. Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of Networks. Oxford University Press, New York (2003)
6. Douglas, C.C., Miranker, W.L.: Constructive interference in parallel algorithms. SIAM J. Numer. Analysis 25(2), 376-398 (1988)
7. Golub, G.H., van Loan, C.F.: Matrix Computations, 3rd edn. Johns Hopkins, Baltimore (1996)
8. Kumar, S. D., et al.: Exploiting the block structure of the Web for computing PageRank. Stanford University Technical Report (2003), http://citeseer.ist.psu.edu/kamvar03exploiting.html
9. Hackbusch, W.: Iterative Lösung großer schwachbesetzter Gleichungssysteme. Teubner, Stuttgart (1991)
10. Haviv, M.: Aggregation/disaggregation methods for computing the stationary distribution of a Markov chain. SIAM J. Numer. Analysis 24(4), 952-966 (1987) (Pubitemid 17637140)
11. Horton, G., Leutenegger, S.: A multilevel solution algorithm for steady-state Markov chains. In: Proc. SIGMETRICS 1994, Nashville, May 16-20 (1994)
12. Kammenhuber, N., Luxenburger, J., Feldmann, A., Weikum, G.: Web search clickstreams. In: Internet Measurement Conference 2006, pp. 245-250 (2006) (Pubitemid 47165605)
13. Krashakov, S.A., Teslyuk, A.B., Shchur, L.N.: On the universality of rank distributions of website popularity. Computer Networks 50(11), 1769-1780 (2006) (Pubitemid 43816901)
14. Krieger, U.R., Müller-Clostermann, B., Sczittnick, M.: Modeling and analysis of communication systems based on computational methods for Markov chains. IEEE Journal on Selected Areas in Communications 8(9), 1630-1648 (1990)
15. Krieger, U.R.: On a two-level multigrid solution method for finite Markov chains. Linear Algebra and its Applications 223/224, 415-438 (1995)
16. Krieger, U.R.: Numerical solution of large finite Markov chains by algebraic multigrid techniques. In: Stewart, W.J. (ed.) Computations with Markov Chains, pp. 403-424. Kluwer, Boston (1995)
17. Langville, A.N., Meyer, C.D.: Google's Pagerank and Beyond: The Science of Search Engine Rankings. Princeton University Press, Princeton (2006)
18. Lempel, R., Moran, S.: SALSA : The stochastic approach for link-structure analysis. ACM Trans. Information Systems 19, 131-160 (2001) (Pubitemid 33720981)
19. Mandel, J., Sekerka, B.: A local convergence proof for the iterative aggregation method. Linear Algebra and its Applications 51, 163-172 (1983)
20. Ng, A.Y., et al.: Stable algorithms for link analysis. In: Proc. 24th Ann. Int. ACM SIGIR Conf., pp. 258-266 (2001) (Pubitemid 32951079)
21. Schneider, H.: Theorems on M-splittings of a singular M-matrix which depend on graph structure. Linear Algebra and its Applications 58, 407-424 (1984)
22. Schweitzer, P.J.: A survey of aggregation-disaggregation in large Markov chains. In: Stewart, W.J. (ed.) Numerical Solution of Markov Chains, pp. 63-88. Marcel Dekker, New York (1991)
23. Schweitzer, P.J., Kindle, K.W.: An iterative aggregation-disaggregation algorithm for solving linear equations. Applied Mathematics and Computation 18, 313-353 (1986)
24. Wang, Q., et al.: Improving link analysis through considering hosts and blocks. In: Proc. IEEE/WIC/ACM Int. Conference on Web Intelligence 2006 (2006)