Advertisement

The Robot Crawler Model on Complete k-Partite and Erdős-Rényi Random Graphs

  • A. DavidsonEmail author
  • A. Ganesh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11631)

Abstract

Web crawlers are used by internet search engines to gather information about the web graph. In this paper we investigate a simple process which models such software by walking around the vertices of a graph. Once initial random vertex weights have been assigned, the robot crawler traverses the graph deterministically following a greedy algorithm, always visiting the neighbour of least weight and then updating this weight to be the highest overall. We consider the maximum, minimum and average number of steps taken by the crawler to visit every vertex of firstly, sparse Erdős-Rényi random graphs and secondly, complete k-partite graphs. Our work is closely related to a paper of Bonato et al. who introduced the model.

MSC2010 Subject Classification.

60C05 05C80 05C81 05C85 90B15 

References

  1. 1.
    Berenbrink, P., Cooper, C., Friedetzky, T.: Random walks which prefer unvisited edges: exploring high girth even degree expanders in linear time. Random Struct. Algorithms 46(1), 36–54 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bollobás, B.: The diameter of random graphs. Trans. Am. Math. Soc. 267(1), 41–52 (1981)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bonato, A., del Río-Chanona, R.M., MacRury, C., Nicolaidis, J., Pérez-Giménez, X., Prałat, P., Ternovsky, K.: The robot Crawler number of a graph. In: Gleich, D.F., Komjáthy, J., Litvak, N. (eds.) WAW 2015. LNCS, vol. 9479, pp. 132–147. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-26784-5_11CrossRefzbMATHGoogle Scholar
  4. 4.
    Brin, S., Page, L.: Anatomy of a large-scale hypertextual web search engine. In: 7th International World Wide Web Conference (1998)Google Scholar
  5. 5.
    Chung, F., Linyuan, L.: The diameter of sparse random graphs. Adv. Appl. Math. 26(4), 257–279 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Godrèche, C., Majumdar, S.N., Schehr, G.: Record statistics for random walk bridges. J. Stat. Mech.: Theory Exp. 2015(7), P07026 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Henzinger, M.R.: Algorithmic challenges in web search engines. Internet Math. 1(1), 115–123 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Messinger, M.-E., Nowakowski, R.J.: The robot cleans up. In: Yang, B., Du, D.-Z., Wang, C.A. (eds.) COCOA 2008. LNCS, vol. 5165, pp. 309–318. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-85097-7_29CrossRefGoogle Scholar
  9. 9.
    Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  10. 10.
    Olston, C., Najork, M.: Web crawling. Found. Trends Inf. Retr. 4(3), 175–246 (2010)CrossRefGoogle Scholar
  11. 11.
    Orenshtein, T., Shinkar, I.: Greedy random walk. Comb. Probab. Comput. 23(02), 269–289 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of MathematicsUniversity of BristolBristolUK

Personalised recommendations