Fault Tolerant Network Constructors

  • Othon MichailEmail author
  • Paul G. SpirakisEmail author
  • Michail TheofilatosEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11914)


In this work, we consider adversarial crash faults of nodes in the network constructors model [Michail and Spirakis, 2016]. We first show that, without further assumptions, the class of graph languages that can be (stably) constructed under crash faults is non-empty but small. When there is a finite upper bound f on the number of faults, we show that it is impossible to construct any non-hereditary graph language and leave as an interesting open problem the hereditary case. On the positive side, by relaxing our requirements we prove that: (i) permitting linear waste enables to construct on \(n/(2f)-f\) nodes, any graph language that is constructible in the fault-free case, (ii) partial constructibility (i.e., not having to generate all graphs in the language) allows the construction of a large class of graph languages. We then extend the original model with a minimal form of fault notifications, and our main result here is a fault-tolerant universal constructor that requires linear waste in the population. Finally, we show that logarithmic local memories can be exploited for a no-waste fault-tolerant simulation of any such protocol.


Network construction Distributed protocol Self stabilization Fault tolerant protocol Dynamic graph formation Fairness Self-organization 


  1. [AAD+06]
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distrib. Comput. 18(4), 235–253 (2006)zbMATHGoogle Scholar
  2. [AAER07]
    Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distrib. Comput. 20(4), 279–304 (2007)zbMATHGoogle Scholar
  3. [AAFJ08]
    Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. ACM Trans. Auton. Adapt. Syst. 3(4), 1–28 (2008)Google Scholar
  4. [BBB13]
    Beauquier, J., Blanchard, P., Burman, J.: Self-stabilizing leader election in population protocols over arbitrary communication graphs. In: Baldoni, R., Nisse, N., van Steen, M. (eds.) OPODIS 2013. LNCS, vol. 8304, pp. 38–52. Springer, Cham (2013). Scholar
  5. [CLV+17]
    Cooper, C., Lamani, A., Viglietta, G., Yamashita, M., Yamauchi, Y.: Constructing self-stabilizing oscillators in population protocols. Inf. Comput. 255, 336–351 (2017)MathSciNetzbMATHGoogle Scholar
  6. [DDG+14]
    Derakhshandeh, Z., Dolev, S., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Brief announcement: amoebot-a new model for programmable matter. In: Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures, pp. 220–222. ACM (2014)Google Scholar
  7. [DDG+18]
    Daymude, J.J., et al.: On the runtime of universal coating for programmable matter. Nat. Comput. 17(1), 81–96 (2018)MathSciNetGoogle Scholar
  8. [DGFGR06]
    Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Ruppert, E.: When birds die: making population protocols fault-tolerant. In: Gibbons, P.B., Abdelzaher, T., Aspnes, J., Rao, R. (eds.) DCOSS 2006. LNCS, vol. 4026, pp. 51–66. Springer, Heidelberg (2006). Scholar
  9. [DIM93]
    Dolev, S., Israeli, A., Moran, S.: Self-stabilization of dynamic systems assuming only read/write atomicity. Distrib. Comput. 7(1), 3–16 (1993)zbMATHGoogle Scholar
  10. [DLFI+17]
    Di Luna, G.A., Flocchini, P., Izumi, T., Izumi, T., Santoro, N., Viglietta, G.: Population protocols with faulty interactions: the impact of a leader. In: Fotakis, D., Pagourtzis, A., Paschos, V.T. (eds.) CIAC 2017. LNCS, vol. 10236, pp. 454–466. Springer, Cham (2017). Scholar
  11. [DLFS+19]
    Di Luna, G.A., Flocchini, P., Santoro, N., Viglietta, G., Yamauchi, Y.: Shape formation by programmable particles. Distrib. Comput. 1–33 (2019)Google Scholar
  12. [Dol00]
    Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  13. [DT01]
    Ducourthial, B., Tixeuil, S.: Self-stabilization with r-operators. Distrib. Comput. 14(3), 147–162 (2001)zbMATHGoogle Scholar
  14. [GK10]
    Guellati, N., Kheddouci, H.: A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs. J. Parallel Distrib. Comput. 70(4), 406–415 (2010)zbMATHGoogle Scholar
  15. [GKR10]
    Gilpin, K., Knaian, A., Rus, D.: Robot pebbles: one centimeter modules for programmable matter through self-disassembly. In: 2010 IEEE International Conference on Robotics and Automation (ICRA), pp. 2485–2492. IEEE (2010)Google Scholar
  16. [GR09]
    Guerraoui, R., Ruppert, E.: Names trump malice: tiny mobile agents can tolerate byzantine failures. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 484–495. Springer, Heidelberg (2009). Scholar
  17. [MCS11]
    Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Mediated population protocols. Theoret. Comput. Sci. 412(22), 2434–2450 (2011)MathSciNetzbMATHGoogle Scholar
  18. [Mic18]
    Michail, O.: Terminating distributed construction of shapes and patterns in a fair solution of automata. Distrib. Comput. 31(5), 343–365 (2018)MathSciNetzbMATHGoogle Scholar
  19. [MOKY12]
    Mizoguchi, R., Ono, H., Kijima, S., Yamashita, M.: On space complexity of self-stabilizing leader election in mediated population protocol. Distrib. Comput. 25(6), 451–460 (2012)zbMATHGoogle Scholar
  20. [MS16]
    Michail, O., Spirakis, P.G.: Simple and efficient local codes for distributed stable network construction. Distrib. Comput. 29(3), 207–237 (2016)MathSciNetzbMATHGoogle Scholar
  21. [MS17]
    Michail, O., Spirakis, P.G.: Network constructors: a model for programmable matter. In: Steffen, B., Baier, C., van den Brand, M., Eder, J., Hinchey, M., Margaria, T. (eds.) SOFSEM 2017. LNCS, vol. 10139, pp. 15–34. Springer, Cham (2017). Scholar
  22. [MSS19]
    Michail, O., Skretas, G., Spirakis, P.G.: On the transformation capability of feasible mechanisms for programmable matter. J. Comput. Syst. Sci. 102, 18–39 (2019)MathSciNetzbMATHGoogle Scholar
  23. [MST19]
    Michail, O., Spirakis, P.G., Theofilatos, M.: Fault tolerant network constructors. arXiv preprint arXiv:1903.05992 (2019)
  24. [Pel09]
    Peleg, D.: As good as it gets: competitive fault tolerance in network structures. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 35–46. Springer, Heidelberg (2009). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  2. 2.Computer Engineering and Informatics DepartmentUniversity of PatrasPatrasGreece

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