Gathering of Mobile Agents in Asynchronous Byzantine Environments with Authenticated Whiteboards

  • Masashi Tsuchida
  • Fukuhito Ooshita
  • Michiko Inoue
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11028)


We propose two algorithms for the gathering problem of k mobile agents in asynchronous Byzantine environments. For both algorithms, we assume that graph topology is arbitrary, each node is equipped with an authenticated whiteboard, agents have unique IDs, and at most f weakly Byzantine agents exist. Under these assumptions, the first algorithm achieves the gathering without termination in \(O(m+fn)\) moves per agent (m is the number of edges and n is the number of nodes). The second algorithm achieves the gathering with termination in \(O(m+fn)\) moves per agent by additionally assuming that agents on the same node are synchronized, \(f<\lceil \frac{1}{3} k \rceil \) holds, and agents know k. To the best of our knowledge, this is the first work to address the gathering problem of mobile agents for arbitrary topology networks in asynchronous Byzantine environments.


  1. 1.
    Bouchard, S., Dieudonné, Y., Ducourthial, B.: Byzantine gathering in networks. Distrib. Comput. 29(6), 435–457 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cao, J., Das, S.K.: Mobile Agents in Networking and Distributed Computing. Wiley, Hoboken (2012)CrossRefGoogle Scholar
  3. 3.
    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). Scholar
  4. 4.
    Czyzowicz, J., Kosowski, A., Pelc, A.: How to meet when you forget: log-space rendezvous in arbitrary graphs. Distrib. Comput. 25(2), 165–178 (2012)CrossRefGoogle Scholar
  5. 5.
    Czyzowicz, J., Kosowski, A., Pelc, A.: Time versus space trade-offs for rendezvous in trees. Distrib. Comput. 27(2), 95–109 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Das, S., Luccio, F.L., Markou, E.: Mobile agents rendezvous in spite of a malicious agent. In: Bose, P., Gąsieniec, L.A., Römer, K., Wattenhofer, R. (eds.) ALGOSENSORS 2015. LNCS, vol. 9536, pp. 211–224. Springer, Cham (2015). Scholar
  7. 7.
    De Marco, G., Gargano, L., Kranakis, E., Krizanc, D., Pelc, A., Vaccaro, U.: Asynchronous deterministic rendezvous in graphs. Theor. Comput. Sci. 355(3), 315–326 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dessmark, A., Fraigniaud, P., Kowalski, D.R., Pelc, A.: Deterministic rendezvous in graphs. Algorithmica 46(1), 69–96 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Dieudonné, Y., Pelc, A., Peleg, D.: Gathering despite mischief. ACM Trans. Algorithms (TALG) 11(1), 1:1–1:28 (2014)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Dieudonné, Y., Pelc, A., Villain, V.: How to meet asynchronously at polynomial cost. SIAM J. Comput. 44(3), 844–867 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fraigniaud, P., Pelc, A.: Delays induce an exponential memory gap for rendezvous in trees. ACM Trans. Algorithms (TALG) 9(2), 17:1–17:24 (2013)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Kowalski, D.R., Malinowski, A.: How to meet in anonymous network. Theor. Comput. Sci. 399(1–2), 141–156 (2008)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kranakis, E., Krizanc, D., Markou, E.: The mobile agent rendezvous problem in the ring. Synth. Lect. Distrib. Comput. Theory 1(1), 1–122 (2010)CrossRefGoogle Scholar
  14. 14.
    Nakamura, J., Ooshita, F., Kakugawa, H., Masuzawa, T.: A single agent exploration in unknown undirected graphs with whiteboards. IEICE Trans. Fundam. Electron., Commun. Comput. Sci. 98(10), 2117–2128 (2015)Google Scholar
  15. 15.
    Ooshita, F., Kawai, S., Kakugawa, H., Masuzawa, T.: Randomized gathering of mobile agents in anonymous unidirectional ring networks. IEEE Trans. Parallel Distrib. Syst. 25(5), 1289–1296 (2014)CrossRefGoogle Scholar
  16. 16.
    Pelc, A.: Deterministic rendezvous in networks: a comprehensive survey. Networks 59(3), 331–347 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Pelc, A.: Deterministic gathering with crash faults. Networks 72, 182–199 (2018)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Ta-Shma, A., Zwick, U.: Deterministic rendezvous, treasure hunts, and stronglyuniversal exploration sequences. ACM Trans. Algorithms (TALG) 10(3), 12:1–12:15 (2014)zbMATHGoogle Scholar
  19. 19.
    Tsuchida, M., Ooshita, F., Inoue, M.: Byzantine gathering in networks with authenticated whiteboards. In: Poon, S.-H., Rahman, M.S., Yen, H.-C. (eds.) WALCOM 2017. LNCS, vol. 10167, pp. 106–118. Springer, Cham (2017). Scholar
  20. 20.
    Tsuchida, M., Ooshita, F., Inoue, M.: Byzantine gathering in networks with authenticated whiteboards. NAIST Information Science Technical Report (NAIST-IS-TR2018001) (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Masashi Tsuchida
    • 1
  • Fukuhito Ooshita
    • 1
  • Michiko Inoue
    • 1
  1. 1.Nara Institute of Science and TechnologyIkomaJapan

Personalised recommendations