Finding Good Coffee in Paris

  • Paola Flocchini
  • Matthew Kellett
  • Peter C. Mason
  • Nicola Santoro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7288)


Finding a good cup of coffee in Paris is difficult even among its world-renowned cafés, at least according to author David Downie (2011). We propose a solution that would allow tourists to create a map of the Paris Métro system from scratch that shows the locations of the cafés with the good coffee, while addressing the problem of the tourists losing interest in the process once they have found good coffee. We map the problem to the black hole search problem in the subway model introduced by Flocchini et al. at Fun with Algorithms 2010. We provide a solution that allows the tourists to start anywhere and at any time, communicate using whiteboards on the subway trains, rely on much less information than is normally available to subway passengers, and work independently but collectively to map the subway network. Our solution is the first to deal with scattered agents searching for black holes in a dynamic network and is optimal both in terms of the team size and the number of carrier moves required to complete the map.


Black Hole Span Tree Mobile Agent Black Hole Site Carrier Move 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-Varying Graphs and Dynamic Networks. In: Frey, H., Li, X., Ruehrup, S. (eds.) ADHOC-NOW 2011. LNCS, vol. 6811, pp. 346–359. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Chalopin, J., Das, S., Santoro, N.: Rendezvous of Mobile Agents in Unknown Graphs with Faulty Links. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 108–122. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Cooper, C., Klasing, R., Radzik, T.: Searching for Black-Hole Faults in a Network Using Multiple Agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 320–332. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Cooper, C., Klasing, R., Radzik, T.: Locating and Repairing Faults in a Network with Mobile Agents. In: Shvartsman, A.A., Felber, P. (eds.) SIROCCO 2008. LNCS, vol. 5058, pp. 20–32. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Complexity of searching for a black hole. Fund. Inform. 71(2,3), 229–242 (2006)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Searching for a black hole in synchronous tree networks. Combin. Probab. Comput. 16(4), 595–619 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks: Optimal mobile agents protocols. Distrib. Comput. 19(1), 1–19 (2006)CrossRefGoogle Scholar
  8. 8.
    Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Mobile search for a black hole in an anonymous ring. Algorithmica 48(1), 67–90 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Dobrev, S., Santoro, N., Shi, W.: Locating a Black Hole in an Un-oriented Ring Using Tokens: The Case of Scattered Agents. In: Kermarrec, A.-M., Bougé, L., Priol, T. (eds.) Euro-Par 2007. LNCS, vol. 4641, pp. 608–617. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Dobrev, S., Santoro, N., Shi, W.: Using scattered mobile agents to locate a black hole in an un-oriented ring with tokens. Internat. J. Found. Comput. Sci. 19(6), 1355–1372 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Downie, D.: Paris, Paris: Journey into the City of Light. Broadway (2011), ISBN 978-0307886088Google Scholar
  12. 12.
    Flocchini, P., Ilcinkas, D., Santoro, N.: Ping pong in dangerous graphs: Optimal black hole search with pebbles. Algorithmica 1–28 (2011)Google Scholar
  13. 13.
    Flocchini, P., Kellett, M., Mason, P.C., Santoro, N.: Map construction and exploration by mobile agents scattered in a dangerous network. In: Proceedings of IPDPS 2009, pp. 1–10 (2009)Google Scholar
  14. 14.
    Flocchini, P., Kellett, M., Mason, P.C., Santoro, N.: Mapping an Unfriendly Subway System. In: Boldi, P. (ed.) FUN 2010. LNCS, vol. 6099, pp. 190–201. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Flocchini, P., Kellett, M., Mason, P.C., Santoro, N.: Searching for black holes in subways. Theory of Computing Systems 50(1), 158–184 (2012)CrossRefGoogle Scholar
  16. 16.
    Flocchini, P., Mans, B., Santoro, N.: Exploration of Periodically Varying Graphs. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 534–543. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    Glaus, P.: Locating a Black Hole without the Knowledge of Incoming Link. In: Dolev, S. (ed.) ALGOSENSORS 2009. LNCS, vol. 5804, pp. 128–138. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Ilcinkas, D., Wade, A.M.: On the Power of Waiting When Exploring Public Transportation Systems. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 451–464. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  19. 19.
    Klasing, R., Markou, E., Radzik, T., Sarracco, F.: Hardness and approximation results for black hole search in arbitrary networks. Theor. Comput. Sci. 384(2-3), 201–221 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Klasing, R., Markou, E., Radzik, T., Sarracco, F.: Approximation bounds for black hole search problems. Networks 52(4), 216–226 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Kosowski, A., Navarra, A., Pinotti, M.C.: Synchronization Helps Robots to Detect Black Holes in Directed Graphs. In: Abdelzaher, T., Raynal, M., Santoro, N. (eds.) OPODIS 2009. LNCS, vol. 5923, pp. 86–98. Springer, Heidelberg (2009)Google Scholar
  22. 22.
    Shi, W.: Black Hole Search with Tokens in Interconnected Networks. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 670–682. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Paola Flocchini
    • 1
  • Matthew Kellett
    • 2
  • Peter C. Mason
    • 2
  • Nicola Santoro
    • 3
  1. 1.School of Electrical Engineering and Computer ScienceUniversity of OttawaCanada
  2. 2.Defence R&DGovernment of CanadaOttawaCanada
  3. 3.School of Computer ScienceCarleton UniversityCanada

Personalised recommendations