Conscious and Unconscious Counting on Anonymous Dynamic Networks

  • Giuseppe Antonio Di Luna
  • Roberto Baldoni
  • Silvia Bonomi
  • Ioannis Chatzigiannakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8314)

Abstract

This paper addresses the problem of counting the size of a network where (i) processes have the same identifiers (anonymous nodes) and (ii) the network topology constantly changes (dynamic network). Changes are driven by a powerful adversary that can look at internal process states and add and remove edges in order to contrast the convergence of the algorithm to the correct count. The paper proposes two leader-based counting algorithms. Such algorithms are based on a technique that mimics an energy-transfer between network nodes.

The first algorithm assumes that the adversary cannot generate either disconnected network graphs or network graphs where nodes have degree greater than D. In such algorithm, the leader can count the size of the network and detect the counting termination in a finite time (i.e., conscious counting algorithm). The second algorithm assumes that the adversary only keeps the network graph connected at any time and we prove that the leader can still converge to a correct count in a finite number of rounds, but it is not conscious when this convergence happens.

Keywords

Anonymous Networks Dynamic Networks Counting Algorithms Dynamic Graph Adversary 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aguilera, M.K., Keidar, I., Malkhi, D., Shraer, A.: Dynamic atomic storage without consensus. J. ACM 58(2), 7 (2011)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Angluin, D.: Local and global properties in networks of processors (extended abstract). In: STOC, pp. 82–93. ACM (1980)Google Scholar
  3. 3.
    Aspnes, J., Fich, F.E., Ruppert, E.: Relationships between broadcast and shared memory in reliable anonymous distributed systems. Distrib. Comput. 18(3), 209–219 (2006)CrossRefGoogle Scholar
  4. 4.
    Attiya, H., Snir, M., Warmuth, M.K.: Computing on an anonymous ring. J. ACM 35(4), 845–875 (1988)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Baldoni, R., Bertier, M., Raynal, M., Tucci-Piergiovanni, S.: Looking for a definition of dynamic distributed systems. In: Malyshkin, V.E. (ed.) PaCT 2007. LNCS, vol. 4671, pp. 1–14. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Baldoni, R., Bonomi, S., Raynal, M.: Implementing a Regular Register in an Eventually Synchronous Distributed System Prone to Continuous Churn. IEEE Transaction on Parallel Distributed Systems 23(1), 102–109 (2012)CrossRefGoogle Scholar
  7. 7.
    Boldi, P., Vigna, S.: Computing anonymously with arbitrary knowledge. In: PODC, pp. 181–188. ACM (1999)Google Scholar
  8. 8.
    Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. CoRR, abs/1012.0009 (2010)Google Scholar
  9. 9.
    Chalopin, J., Métivier, Y., Morsellino, T.: On snapshots and stable properties detection in anonymous fully distributed systems (Extended abstract). In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 207–218. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Chockler, G., Gilbert, S., Gramoli, V., Musial, P.M., Shvartsman, A.A.: Reconfigurable distributed storage for dynamic networks. J. Parallel Distrib. Comput. 69(1), 100–116 (2009)CrossRefGoogle Scholar
  11. 11.
    Fraigniaud, P., Pelc, A., Peleg, D., Pérennes, S.: Assigning labels in unknown anonymous networks. In: PODC, pp. 101–111. ACM (2000)Google Scholar
  12. 12.
    Jelasity, M., Montresor, A., Babaoglu, Ö.: Gossip-based aggregation in large dynamic networks. ACM Trans. Comput. Syst. 23(3), 219–252 (2005)CrossRefGoogle Scholar
  13. 13.
    Kempe, D., Dobra, A., Gehrke, J.: Gossip-based computation of aggregate information. In: FOCS, pp. 482–491 (2003)Google Scholar
  14. 14.
    Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: STOC, pp. 513–522. ACM, New York (2010)Google Scholar
  15. 15.
    Di Luna, G., Bonomi, S., Chatzigiannakis, I., Baldoni, R.: Counting in Anonymous Dynamic Networks: An Experimental Perspective. In: ALGOSENSORS 2013 (to appear), http://www.dis.uniroma1.it/~midlab/articoli/main_2.pdf
  16. 16.
    Michail, O., Chatzigiannakis, I., Spirakis, P.G.: Naming and counting in anonymous unknown dynamic networks. In: Higashino, T., Katayama, Y., Masuzawa, T., Potop-Butucaru, M., Yamashita, M. (eds.) SSS 2013. LNCS, vol. 8255, pp. 281–295. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  17. 17.
    O’Dell, R., Wattenhofer, R.: Information dissemination in highly dynamic graphs. In: DIALM-POMC, pp. 104–110. ACM, New York (2005)CrossRefGoogle Scholar
  18. 18.
    Yamashita, M., Kameda, T.: Computing on an anonymous network. In: PODC, pp. 117–130. ACM, New York (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Giuseppe Antonio Di Luna
    • 1
  • Roberto Baldoni
    • 1
  • Silvia Bonomi
    • 1
  • Ioannis Chatzigiannakis
    • 2
  1. 1.Cyber Intelligence and Information Security Research Center and Dipartimento di Ingegneria Informatica, Automatica e Gestionale Antonio RubertiUniversitá degli Studi di Roma La SapienzaRomaItaly
  2. 2.Computer Technology Institute & Press “Diophantus” (CTI)PatrasGreece

Personalised recommendations