Deterministic Rendezvous Algorithms

  • Andrzej PelcEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11340)


The task of rendezvous (also called gathering) calls for a meeting of two or more mobile entities, starting from different positions in some environment. Those entities are called mobile agents or robots, and the environment can be a network modeled as a graph or a terrain in the plane, possibly with obstacles. The rendezvous problem has been studied in many different scenarios. Two among many adopted assumptions particularly influence the methodology to be used to accomplish rendezvous. One of the assumptions specifies whether the agents in their navigation can see something apart from parts of the environment itself, for example other agents or marks left by them. The other assumption concerns the way in which the entities move: it can be either deterministic or randomized. In this paper we survey results on deterministic rendezvous of agents that cannot see the other agents prior to meeting them, and cannot leave any marks.


Mobile agent Rendezvous Deterministic Network Graph Terrain Plane 


  1. 1.
    Alpern, S.: Rendezvous search: a personal perspective. Oper. Res. 50, 772–795 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. International Series in Operations Research and Management Science. Kluwer Academic Publishers, Norwell (2003)zbMATHGoogle Scholar
  3. 3.
    Baba, D., Izumi, T., Ooshita, F., Kakugawa, H., Masuzawa, T.: Linear time and space gathering of anonymous mobile agents in asynchronous trees. Theor. Comput. Sci. 478, 118–126 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bampas, E., Czyzowicz, J., Gąsieniec, L., Ilcinkas, D., Labourel, A.: Almost optimal asynchronous rendezvous in infinite multidimensional grids. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 297–311. Springer, Heidelberg (2010). Scholar
  5. 5.
    Bouchard, S., Dieudonné, Y., Ducourthial, B.: Byzantine gathering in networks. Distrib. Comput. 29, 435–457 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bouchard, S., Bournat, M., Dieudonné, Y., Dubois, S., Petit, F.: Asynchronous approach in the plane: a deterministic polynomial algorithm. In: Proceedings of 31st International Symposium on Distributed Computing (DISC 2017), pp. 8:1–8:16 (2017)Google Scholar
  7. 7.
    Bouchard, S., Dieudonné, Y., Lamani, A.: Byzantine gathering in polynomial time. In: Proceedings of 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018), pp. 147:1–147:15 (2018)Google Scholar
  8. 8.
    Bouchard, S., Dieudonné, Y., Pelc, A., Petit, F.: Deterministic rendezvous at a node of agents with arbitrary velocities. Inf. Process. Lett. 133, 39–43 (2018)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Chalopin, J., Dieudonné, Y., Labourel, A., Pelc, A.: Rendezvous in networks in spite of delay faults. Distrib. Comput. 29, 187–205 (2016)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Collins, A., Czyzowicz, J., Gąsieniec, L., Labourel, A.: Tell me where i am so i can meet you sooner. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 502–514. Springer, Heidelberg (2010). Scholar
  11. 11.
    Cornejo, A., Kuhn, F.: Deploying wireless networks with beeps. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 148–162. Springer, Heidelberg (2010). Scholar
  12. 12.
    Czyzowicz, J., Kosowski, A., Pelc, A.: How to meet when you forget: log-space rendezvous in arbitrary graphs. Distrib. Comput. 25, 165–178 (2012)CrossRefGoogle Scholar
  13. 13.
    Czyzowicz, J., Kosowski, A., Pelc, A.: Time vs. space trade-offs for rendezvous in trees. Distrib. Comput. 27, 95–109 (2014)Google Scholar
  14. 14.
    Czyzowicz, J., Kosowski, A., Pelc, A.: Deterministic rendezvous of asynchronous bounded-memory agents in polygonal terrains. Theory Comput. Syst. 52, 179–199 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Czyzowicz, J., Labourel, A., Pelc, A.: How to meet asynchronously (almost) everywhere. ACM Trans. Algorithms 8, 37:1–37:14 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Das, S., Dereniowski, D., Kosowski, A., Uznański, P.: Rendezvous of distance-aware mobile agents in unknown graphs. In: Halldórsson, M.M. (ed.) SIROCCO 2014. LNCS, vol. 8576, pp. 295–310. Springer, Cham (2014). Scholar
  17. 17.
    De Marco, G., Gargano, L., Kranakis, E., Krizanc, D., Pelc, A., Vaccaro, U.: Asynchronous deterministic rendezvous in graphs. Theoret. Comput. Sci. 355, 315–326 (2006)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Dessmark, A., Fraigniaud, P., Kowalski, D., Pelc, A.: Deterministic rendezvous in graphs. Algorithmica 46, 69–96 (2006)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Dieudonné, Y., Pelc, A.: Anonymous meeting in networks. Algorithmica 74, 908–946 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Dieudonné, Y., Pelc, A.: Deterministic polynomial approach in the plane. Distrib. Comput. 28, 111–129 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Dieudonné, Y., Pelc, A.: Price of asynchrony in mobile agents computing. Theoret. Comput. Sci. 524, 59–67 (2014)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Dieudonné, Y., Pelc, A., Peleg, D.: Gathering despite mischief. ACM Trans. Algorithms 11, 1:1–1:28 (2014)Google Scholar
  23. 23.
    Dieudonné, Y., Pelc, A., Villain, V.: How to meet asynchronously at polynomial cost. SIAM J. Comput. 44, 844–867 (2015)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Elouasbi, S., Pelc, A.: Deterministic rendezvous with detection using beeps. Int. J. Found. Comput. Sci. 28, 77–97 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Elouasbi, S., Pelc, A.: Deterministic meeting of sniffing agents in the plane. Fundam. Informaticae 160, 281–301 (2018)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Elouasbi, S., Pelc, A.: Time of anonymous rendezvous in trees: determinism vs. randomization. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 291–302. Springer, Heidelberg (2012). Scholar
  27. 27.
    Fraigniaud, P., Pelc, A.: Delays induce an exponential memory gap for rendezvous in trees. ACM Trans. Algorithms 9, 17:1–17:24 (2013)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Guilbault, S., Pelc, A.: Asynchronous rendezvous of anonymous agents in arbitrary graphs. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 421–434. Springer, Heidelberg (2011). Scholar
  29. 29.
    Kouckỳ, M.: Universal traversal sequences with backtracking. J. Comput. Syst. Sci. 65, 717–726 (2002)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Kowalski, D., Malinowski, A.: How to meet in anonymous network. Theoret. Comput. Sci. 399, 141–156 (2008)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Kranakis, E., Krizanc, D., Markou, E.: The Mobile Agent Rendezvous Problem in the Ring. Morgan and Claypool Publishers, San Rafael (2010)CrossRefGoogle Scholar
  32. 32.
    Kranakis, E., Krizanc, D., Rajsbaum, S.: Mobile agent rendezvous: a survey. In: Flocchini, P., Gąsieniec, L. (eds.) SIROCCO 2006. LNCS, vol. 4056, pp. 1–9. Springer, Heidelberg (2006). Scholar
  33. 33.
    Miller, A., Pelc, A.: Time versus cost tradeoffs for deterministic rendezvous in networks. Distrib. Comput. 29, 51–64 (2016)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Miller, A., Pelc, A.: Fast rendezvous with advice. Theoret. Comput. Sci. 608, 190–198 (2015)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Ooshita, F., Datta, A.K., Masuzawa, T.: Self-stabilizing rendezvous of synchronous mobile agents in graphs. In: Spirakis, P., Tsigas, P. (eds.) SSS 2017. LNCS, vol. 10616, pp. 18–32. Springer, Cham (2017). Scholar
  36. 36.
    Pelc, A.: Deterministic rendezvous in networks: a comprehensive survey. Networks 59, 331–347 (2012)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Pelc, A.: Deterministic gathering with crash faults, CoRR abs/1704.08880 (2017)Google Scholar
  38. 38.
    Reingold, O.: Undirected connectivity in log-space. J. ACM 55, 1–24 (2008)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Schelling, T.: The Strategy of Conflict. Oxford University Press, Oxford (1960)zbMATHGoogle Scholar
  40. 40.
    Stachowiak, G.: Asynchronous deterministic rendezvous on the line. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds.) SOFSEM 2009. LNCS, vol. 5404, pp. 497–508. Springer, Heidelberg (2009). Scholar
  41. 41.
    Ta-Shma, A., Zwick, U.: Deterministic rendezvous, treasure hunts and strongly universal exploration sequences. ACM Trans. Algorithms 10, 12:1–12:15 (2014)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Yamashita, M., Kameda, T.: Computing on anonymous networks: part i-characterizing the solvable cases. IEEE Trans. Parallel Distrib. Syst. 7, 69–89 (1996)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Département d’informatiqueUniversité du Québec en OutaouaisGatineauCanada

Personalised recommendations