Asymptotic analysis for personalized web search

Advances in Applied Probability

Volumn 42, Issue 2, 2010, Pages 577-604

  Volkovich, Yana ^a   Litvak, Nelly ^b  

^a Barcelona Media Innovation Center   (Spain)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Pagerank; Regular variation; Stochastic equation; Tauberian theorem; Web

Indexed keywords

PAGERANK; REGULAR VARIATIONS; STOCHASTIC EQUATIONS; TAUBERIAN THEOREM; WEB;

ASYMPTOTIC ANALYSIS; RANDOM VARIABLES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

WORLD WIDE WEB;

EID: 78650925920     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1275055243     Document Type: Article

References (40)

1. Andersen, R., Chung, F. and Lang, K. (2006). Local graph partitioning using PageRank vectors. In Proc. FOCS 2006, IEEE Computer Society,Washington, DC, pp. 475-486.
2. Andersen, R., Chung, F. and Lang, K. (2007). Local partitioning for directed graphs using PageRank. In Algorithms and Models for the Web-Graph (Lecture Notes Comput. Sci. 4863), Springer, Berlin, pp. 166-178.
3. Avrachenkov, K. and Lebedev, D. (2006). PageRank of scale-free growing networks. Internet Math. 3, 207-231.
4. Avrachenkov, K., Litvak, N. and Pham, K. S. (2007). Distribution of PageRank mass among principle components of the web. In Algorithms and Models for the Web-Graph (Lecture Notes Comput. Sci. 4863), Springer, Berlin, pp. 16-28.
5. Barabási, A.-L. and Albert, R. (1999). Emergence of scaling in random networks. Science 286, 509-512.
6. Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1989). Regular Variation. Cambridge University Press.
7. Boldi, P., Santini, M. and Vigna, S. (2005). PageRank as a function of the damping factor. In Proc. 14th Internat. Conf. World Wide Web, ACM, New York, pp. 557-566.
8. Brin, S. and Page, L. (1998). The anatomy of a large-scale hypertextual Web search engine. Comput. Networks ISDN Systems 30, 107-117.
9. Broder, A. et al. (2000). Graph structure in the Web. Comput. Networks 33, 309-320.
10. Chen, P., Xie, H., Maslov, S. and Redner, S. (2007). Finding scientific gems with Google's PageRank algorithm. J. Informetrics 1, 8-15.
11. Constantine, P. G. and Gleich, D. F. (2007). Using polynomial chaos to compute the influence of multiple random surfers in the PageRank model. In Algorithms and Models for the Web-Graph (Lecture Notes Comput. Sci. 4863), Springer, Berlin, pp. 82-95.
12. De Meyer, A. and Teugels, J. L. (1980). On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1. J. Appl. Prob. 17, 802-813.
13. Fortunato, S. and Flammini, A. (2007). Random walks on directed networks: The case of PageRank. Internat. J. Bifur. Chaos Appl. Sci. Eng. 17, 2343-2353.
14. Fortunato, S., Boguná, M., Flammini, A. and Menczer, F. (2006). Approximating PageRank from indegree. In Algorithms and Models for the Web-Graph (Lecture Notes Comput. Sci. 4936), Springer, Berlin, pp. 59-71.
15. Gyöngyi, Z., Garcia-Molina, H. and Pedersen, J. (2004). Combating Web spam with TrustRank. In Proc. 13th Internat. Conf. Very Large Data Bases, VLDB Endowment, pp. 576-587.
16. Haveliwala, T. H. (2003). Topic-sensitive PageRank: A context-sensitive ranking algorithm for Web search. IEEE Trans. Knowledge Data Eng. 15, 784-796.
17. Haveliwala, T. H., Kamvar, A. and Jeh, G. (2003). An analytical comparison of approaches to personalizing PageRank. Tech. Rep., Stanford University.
18. Jeh, G. andWidom, J. (2003). Scaling personalized Web search. In Proc. 12th Internat. Conf. World Wide Web, ACM, New York, pp. 271-279.
19. Jelenkovic, P. R. and Olvera-Cravioto, M. (2009). Information ranking and power laws on trees. Preprint. Available at http://arxiv.org/abs/0905.1738.
20. Jessen, A. H. and Mikosch, T. (2006). Regularly varying functions. Publ. Inst. Math. (Beograd) (N.S.) 80, 171-192.
21. Kamvar, S. D., Haveliwala, T. H., Manning, C. D. and Golub, G. H. (2003). Exploiting the block structure of the Web for computing. Tech. Rep., Stanford University.
22. Kleinberg, J. M. (1999). Authoritative sources in a hyperlinked environment. J. ACM 46, 604-632.
23. Kraaij, W., Westerveld, T. and Hiemstra, D. (2002). The importance of prior probabilities for entry page search. In Proc. 25th Annual Internat. ACM SIGIR Conf. Research and Development in Information Retrieval, ACM, New York, pp. 27-34.
24. Langville, A. N. and Meyer, C. D. (2006). Google's PageRank and Beyond: The Science of Search Engine Rankings. Princeton University Press.
25. Leskovec, J. and Faloutsos, C. (2006). Sampling from large graphs. In Proc. 12th ACM SIGKDD Internat. Conf. Knowledge Discovery and Data Mining, ACM, New York, pp. 631-636.
26. Litvak, N., Scheinhardt,W. R.W. and Volkovich, Y. (2007). In-degree and PageRank: Why do they follow similar power laws? Internet Math. 4, 175-198.
27. Litvak, N., Scheinhardt, W., Volkovich, Y. and Zwart, B. (2009). Characterization of tail dependence for in-degree and PageRank. In Algorithms and Models for the Web-Graph (Lecture Notes Comput. Sci. 5427), Springer, Berlin, pp. 90-103.
28. Liu,Q. (1998). Fixed points of a generalized smoothing transformation and applications to the branching random walk. Adv. Appl. Prob. 30, 85-112.
29. Liu, Q. (2001). Asymptotic properties and absolute continuity of laws stable by random weighted mean. Stoch. Process. Appl. 95, 83-107.
30. Micarelli, A., Gasparetti, F., Sciarrone, F. and Gauch, S. (2007). Personalized search on the World Wide Web. In The Adaptive Web (Lecture Notes Comput. Sci. 4321), Springer, Berlin, pp. 195-230.
31. Page, L., Brin, S., Motwani, R. andWinograd, T. (1998). The PageRank citation ranking: Bringing order to the Web. Tech. Rep., Stanford Digital Library Technologies Project.
32. Pandurangan, G., Raghavan, P. and Upfal, E. (2002). Using PageRank to characterize Web structure. In Computing and Combinatorics (Lecture Notes Comput. Sci. 2387), Springer, Berlin, pp. 330-339.
33. Ponte, J. M. and Croft, W. B. (1998). A language modeling approach to information retrieval. In Proc. 21st Annual Internat. ACM SIGIR Conf. Research and Development in Information Retrieval. ACM, New York, pp. 275-281.
34. Resnick, S. I. (2007). Heavy-tail Phenomena. Springer, New York.
35. Richardson,M. and Domingos, P. (2002). The intelligent surfer: Probabilistic combination of link and content information in PageRank. Adv. NIPS 14, 1441-1448.
36. Ross, S. M. (2003). The inspection paradox. Prob. Eng. Inform. Sci. 17, 47-51.
37. Volkovich, Y., Litvak, N. and Donato, D. (2007). Determining factors behind the PageRank log-log plot. In Algorithms and Models for the Web-Graph (Lecture Notes Comput. Sci. 4863), Springer, Berlin, pp. 108-123.
38. Volkovich, Y., Litvak, N. and Zwart, B. (2008). A framework for evaluating statistical dependencies and rank correlations in power law graphs. Memorandum 1868. University of Twente Enschede.
39. Volkovich, Y., Litvak, N. and Zwart, B. (2009). Extremal dependencies and rank correlations in power law networks. In Complex Sciences, Springer, Berlin, pp. 1642-1653.
40. Zwart, A. P. (2001). Queueing systems with heavy tails. Doctoral Thesis, Eindhoven University of Technology.