Specialist Cops Catching Robbers on Complex Networks

  • Shiraj Arora
  • Abhishek Jain
  • Yenda Ramesh
  • M. V. Panduranga RaoEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 812)


We study a variant of the folklore Cops and Robbers (also known as pursuit evasion) problem on graphs. In this variant, there are different specializations of cops and a minimum number of each specialization are necessary to catch a robber. To the best of our knowledge, this variant has not been investigated so far. We believe that this problem will find relevance in several domains like biological systems and epidemic response strategies. We seek to compare the ease of catching robbers executing random walks on various graphs, especially complex networks. We use Statistical Model Checking for the analysis. In this initial work, we report experiments that yield interesting results. For example, we show empirically that it is easier to catch robbers on the Barabási-Albert model, than on the Erdős-Rényi model.


Cops and Robbers on graphs Statistical model checking Complex networks 


  1. 1.
    Adler, M., Räcke, H., Sivadasan, N., Sohler, C., Vöcking, B.: Randomized pursuit-evasion in graphs. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds.) Automata, Languages and Programming, pp. 901–912. Springer, Berlin Heidelberg, Berlin, Heidelberg (2002)Google Scholar
  2. 2.
    Agha, G., Palmskog, K.: A survey of statistical model checking. ACM Trans. Model. Comput. Simul. 28(1), 6:1–6, 39 (2018). Scholar
  3. 3.
    Aigner, M., Fromme, M.: A game of cops and robbers. Discret. Appl. Math. 8(1), 1–12 (1984)Google Scholar
  4. 4.
    Alspach, B.: Searching and sweeping graphs: a brief survey. Le Matematiche 59, 5–37 (2004)Google Scholar
  5. 5.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999).
  6. 6.
    Chung, T.H., Hollinger, G.A., Isler, V.: Search and pursuit-evasion in mobile robotics. Auton. Robot. 31(4), 299 (2011).
  7. 7.
    Clarke, E.M., Zuliani, P.: Statistical model checking for cyber-physical systems. In: Bultan, T., Hsiung, P.A. (eds.) Automated Technology for Verification and Analysis, pp. 1–12. Springer, Berlin Heidelberg, Berlin, Heidelberg (2011)Google Scholar
  8. 8.
    Cooper, C., Frieze, A., Radzik, T.: Multiple random walks and interacting particle systems. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) Automata, Languages and Programming, pp. 399–410. Springer, Berlin Heidelberg, Berlin, Heidelberg (2009)Google Scholar
  9. 9.
    Erdős, P., Rényi, A.: On the evolution of random graphs. In: Publication of the Mathematical Institute of the Hungarian Academy of Science, pp. 17–61 (1960)Google Scholar
  10. 10.
    Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399, 236–245 (2008)Google Scholar
  11. 11.
    Legay, A., Delahaye, B., Bensalem, S.: Statistical model checking: an overview. In: Barringer, H., et al. (eds.) Runtime Verification. Lecture Notes in Computer Science, vol. 6418, pp. 122–135. Springer, Berlin Heidelberg (2010)Google Scholar
  12. 12.
    Nimal, V.: Statistical approaches for probabilistic model checking. Ph.D. thesis, University of Oxford (2010)Google Scholar
  13. 13.
    Nowakowski, R., Winkler, P.: Vertex-to-vertex pursuit in a graph. Discret. Math. 43(2–3), 235–239 (1983)Google Scholar
  14. 14.
    Quilliot, A.: Problemes de jeux, de point fixe, de connectivité et de représentation sur des graphes, des ensembles ordonnés et des hypergraphes, pp. 131–145. These d’Etat, Université de Paris VI pp (1983)Google Scholar
  15. 15.
    Sen, K., Viswanathan, M., Agha, G.: Computer Aided Verification: 16th International Conference, CAV 2004, Boston, MA, USA, 13–17 July 2004. Proceedings, chap. Statistical Model Checking of Black-Box Probabilistic Systems, pp. 202–215. Springer Berlin Heidelberg, Berlin, Heidelberg (2004)Google Scholar
  16. 16.
    Sen, K., Viswanathan, M., Agha, G.: On statistical model checking of stochastic systems. In: 17th Intlernational Conference on Computer Aided Verification, CAV 2005, Edinburgh, Scotland, UK, 6–10 July 2005, pp. 266–280 (2005)Google Scholar
  17. 17.
    Wald, A.: Sequential tests of statistical hypotheses. Ann. Math. Stat. 16(2), 117–186 (1945)Google Scholar
  18. 18.
    Younes, H.L.: Verification and planning for stochastic processes with asynchronous events. Technical report, Carnegie-Mellon University (2005)Google Scholar
  19. 19.
    Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: 14th International Conference on Computer Aided Verification, CAV 2002, Copenhagen, Denmark, 27–31 July 2002, pp. 223–235 (2002)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Shiraj Arora
    • 1
  • Abhishek Jain
    • 1
  • Yenda Ramesh
    • 1
  • M. V. Panduranga Rao
    • 1
    Email author
  1. 1.Indian Institute of Technology HyderabadSangareddyIndia

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