Skip to main content
SpringerLink
Log in

Gathering in Dynamic Rings

  • Conference paper
  • First Online:
Structural Information and Communication Complexity (SIROCCO 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10641))

Abstract

The gathering (or multi-agent rendezvous) problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced.

The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs.

In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations.

We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem; and we establish several results.

We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather within low polynomial time. In particular, the protocols for gathering with cross detection are time optimal.

We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations.

From our investigation it follows that, for the gathering problem, the computational obstacles created by the dynamic nature of the ring can be overcome by the presence of chirality or of cross-detection.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer, Boston (2003). https://doi.org/10.1007/b100809

    MATH  Google Scholar 

  2. Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Rendezvous and election of mobile agents: impact of sense of direction. Theor. Comput. Syst. 40(2), 143–162 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baston, V., Gal, S.: Rendezvous search when marks are left at the starting points. Naval Res. Logist. 38, 469–494 (1991)

    Article  MATH  Google Scholar 

  4. Biely, M., Robinson, P., Schmid, U., Schwarz, M., Winkler, K.: Gracefully degrading consensus and k-set agreement in directed dynamic networks. In: Bouajjani, A., Fauconnier, H. (eds.) NETYS 2015. LNCS, vol. 9466, pp. 109–124. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26850-7_8

    Chapter  Google Scholar 

  5. Bournat, M., Datta, A.K., Dubois, S.: Self-stabilizing robots in highly dynamic environments. In: Bonakdarpour, B., Petit, F. (eds.) SSS 2016. LNCS, vol. 10083, pp. 54–69. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49259-9_5

    Chapter  Google Scholar 

  6. Bouchard, S., Dieudonne, Y., Ducourthial, B.: Byzantine gathering in networks. Distrib. Comput. 29(6), 435–457 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  7. Casteigts, A., Flocchini, P., Mans, B., Santoro, N.: Measuring temporal lags in delay-tolerant networks. IEEE Trans. Comput. 63(2), 397–410 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. Int. J. Parallel Emergent Distrib. Syst. 27(5), 387–408 (2012)

    Article  Google Scholar 

  9. 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). https://doi.org/10.1007/978-3-540-75142-7_11

    Chapter  Google Scholar 

  10. Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41(4), 829–879 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34, 1516–1528 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Czyzowicz, J., Labourel, A., Pelc, A.: How to meet asynchronously (almost) everywhere. ACM Trans. Algorithms 8(4), 37:1–37:14 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Czyzowicz, J., Dobrev, S., Kranakis, E., Krizanc, D.: The power of tokens: rendezvous and symmetry detection for two mobile agents in a ring. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 234–246. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-77566-9_20

    Chapter  Google Scholar 

  14. Das, S., Luccio, F.L., Focardi, R., Markou, E., Moro, D., Squarcina, M.: Gathering of robots in a ring with mobile faults. In: 17th Italian Conference on Theoretical Computer Science (ICTCS), pp. 122–135 (2016)

    Google Scholar 

  15. 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). https://doi.org/10.1007/978-3-319-28472-9_16

    Chapter  Google Scholar 

  16. Degener, B., Kempkes, B., Langner, T., Meyer auf der Heide, F., Pietrzyk, P., Wattenhofer, R.: A tight runtime bound for synchronous gathering of autonomous robots with limited visibility. In: 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 139–148 (2011)

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  18. Dessmark, A., Fraigniaud, P., Pelc, A.: Deterministic rendezvous in graphs. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 184–195. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-39658-1_19

    Chapter  Google Scholar 

  19. Di Luna, G.A., Dobrev, S., Flocchini, P., Santoro, N.: Live exploration of dynamic rings. In: 36th IEEE International Conference on Distributed Computing Systems, (ICDCS), pp. 570–579 (2016)

    Google Scholar 

  20. Di Luna, G.A., Flocchini, P., Pagli, L., Prencipe, G., Santoro, N., Viglietta, G.: Gathering in dynamic rings. Arxiv, April 2017

    Google Scholar 

  21. Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Multiple agents RendezVous in a ring in spite of a black hole. In: Papatriantafilou, M., Hunel, P. (eds.) OPODIS 2003. LNCS, vol. 3144, pp. 34–46. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27860-3_6

    Chapter  Google Scholar 

  22. Flocchini, P., Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Multiple Mobile Agent Rendezvous in a Ring. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 599–608. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24698-5_62

    Chapter  Google Scholar 

  23. Flocchini, P., Mans, B., Santoro, N.: On the exploration of time-varying networks. Theoret. Comput. Sci. 469, 53–68 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theoret. Comput. Sci. 337(1–3), 147–168 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Flocchini, P., Santoro, N., Viglietta, G., Yamashita, M.: Rendezvous with constant memory. Theoret. Comput. Sci. 621, 57–72 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  26. Haeupler, B., Kuhn, F.: Lower bounds on information dissemination in dynamic networks. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 166–180. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33651-5_12

    Chapter  Google Scholar 

  27. Ilcinkas, D., Klasing, R., Wade, A.M.: Exploration of constantly connected dynamic graphs based on cactuses. In: Halldórsson, M.M. (ed.) SIROCCO 2014. LNCS, vol. 8576, pp. 250–262. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09620-9_20

    Google Scholar 

  28. Ilcinkas, D., Wade, A.M.: Exploration of the T-interval-connected dynamic graphs: the case of the ring. In: Moscibroda, T., Rescigno, A.A. (eds.) SIROCCO 2013. LNCS, vol. 8179, pp. 13–23. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-03578-9_2

    Chapter  Google Scholar 

  29. Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theoret. Comput. Sci. 390(1), 27–39 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  30. Kranakis, E., Krizanc, D., Markou, E.: Mobile agent rendezvous in a synchronous torus. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 653–664. Springer, Heidelberg (2006). https://doi.org/10.1007/11682462_60

    Chapter  Google Scholar 

  31. Kranakis, E., Krizanc, D., Markou, E.: The Mobile Agent Rendezvous Problem in the Ring. Morgan & Claypool (2010)

    Google Scholar 

  32. Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Mobile agent rendezvous problem in the ring. In: 23rd International Conference on Distributed Computing Systems (ICDCS), pp. 592–599 (2003)

    Google Scholar 

  33. Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: 42th Symposium on Theory of Computing (STOC), pp. 513–522 (2010)

    Google Scholar 

  34. Kuhn, F., Moses, Y., Oshman, R.: Coordinated consensus in dynamic networks. In: 30th Symposium on Principles of Distributed Computing (PODC), pp. 1–10 (2011)

    Google Scholar 

  35. Kuhn, F., Oshman, R.: Dynamic networks: models and algorithms. SIGACT News 42(1), 82–96 (2011)

    Article  Google Scholar 

  36. Lin, J., Morse, A.S., Anderson, B.D.O.: The multi-agent rendezvous problem. Parts 1 and 2. SIAM J. Control Optim. 46(6), 2096–2147 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  37. Pagli, L., Prencipe, G., Viglietta, G.: Getting close without touching: near-gathering for autonomous mobile robots. Distrib. Comput. 28(5), 333–349 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  38. Pelc, A.: Deterministic rendezvous in networks: a comprehensive survey. Networks 59(3), 331–347 (2012)

    Article  MathSciNet  Google Scholar 

  39. Sawchuk, C.: Mobile agent rendezvous in the ring. Ph.D Thesis, Carleton University, January 2004

    Google Scholar 

  40. Ta-Shma, A., Zwick, U.: Deterministic rendezvous, treasure hunts, and strongly universal exploration sequences. ACM Trans. Algorithms 10(3), 12 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  41. Yu, X., Yung, M.: Agent rendezvous: a dynamic symmetry-breaking problem. In: Meyer, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 610–621. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61440-0_163

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada

    Giuseppe Antonio Di Luna, Paola Flocchini & Giovanni Viglietta

  2. Dipartimento di Informatica, University of Pisa, Pisa, Italy

    Linda Pagli & Giuseppe Prencipe

  3. School of Computer Science, Carleton University, Ottawa, Canada

    Nicola Santoro

Authors
  1. Giuseppe Antonio Di Luna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paola Flocchini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Linda Pagli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Giuseppe Prencipe
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nicola Santoro
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Giovanni Viglietta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giuseppe Antonio Di Luna .

Editor information

Editors and Affiliations

  1. LIF, Aix-Marseille University, Marseille Cedex 9, France

    Shantanu Das

  2. LIP6, Université Pierre et Marie Curie - Paris 6, Paris, France

    Sebastien Tixeuil

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Di Luna, G.A., Flocchini, P., Pagli, L., Prencipe, G., Santoro, N., Viglietta, G. (2017). Gathering in Dynamic Rings. In: Das, S., Tixeuil, S. (eds) Structural Information and Communication Complexity. SIROCCO 2017. Lecture Notes in Computer Science(), vol 10641. Springer, Cham. https://doi.org/10.1007/978-3-319-72050-0_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-72050-0_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72049-4

  • Online ISBN: 978-3-319-72050-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation