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A Generic Framework for Computing Parameters of Sequence-Based Dynamic Graphs

  • Arnaud CasteigtsEmail author
  • Ralf KlasingEmail author
  • Yessin M. NeggazEmail author
  • Joseph G. PetersEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10641)

Abstract

We presented in [12] an algorithm for computing a parameter called T -interval connectivity of dynamic graphs which are given as a sequence of static graphs. This algorithm operates at a high level, manipulating the graphs in the sequence as atomic elements with two types of operations: a composition operation and a test operation. The algorithm is optimal in the sense that it uses only \(O(\delta )\) composition and test operations, where \(\delta \) is the length of the sequence. In this paper, we generalize this framework to use various composition and test operations, which allows us to compute other parameters using the same high-level strategy that we used for T-interval connectivity. We illustrate the framework through the study of three minimization problems which refer to various properties of dynamic graphs, namely Bounded-Realization-of-the-Footprint, Temporal-Connectivity, and Round-Trip-Temporal-Diameter.

Keywords

Dynamic networks Property testing Generic algorithms Temporal connectivity 

References

  1. 1.
    Aaron, E., Krizanc, D., Meyerson, E.: DMVP: foremost waypoint coverage of time-varying graphs. In: Kratsch, D., Todinca, I. (eds.) WG 2014. LNCS, vol. 8747, pp. 29–41. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-12340-0_3 Google Scholar
  2. 2.
    Awerbuch, B., Even, S.: Efficient and reliable broadcast is achievable in an eventually connected network. In: Proceedings of the Third Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 278–281. ACM (1984)Google Scholar
  3. 3.
    Barjon, M., Casteigts, A., Chaumette, S., Johnen, C., Neggaz, Y.M.: Testing temporal connectivity in sparse dynamic graphs. CoRR abs/1404.7634 (2014). (A French version appeared in Proceedings of ALGOTEL 2014)Google Scholar
  4. 4.
    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 CrossRefGoogle Scholar
  5. 5.
    Bramas, Q., Tixeuil, S.: The complexity of data aggregation in static and dynamic wireless sensor networks. Inf. Comput. 255, 369–383 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Braud-Santoni, N., Dubois, S., Kaaouachi, M.H., Petit, F.: The next 700 impossibility results in time-varying graphs. Int. J. Netw. Comput. 6(1), 27–41 (2016)CrossRefGoogle Scholar
  7. 7.
    Bui-Xuan, B., Ferreira, A., Jarry, A.: Computing shortest, fastest, and foremost journeys in dynamic networks. Int. J. of Found. Comput. Sci. 14(2), 267–285 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Casteigts, A., Chaumette, S., Ferreira, A.: Characterizing topological assumptions of distributed algorithms in dynamic networks. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 126–140. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-11476-2_11. Full version in CoRR, abs/1102.5529CrossRefGoogle Scholar
  9. 9.
    Casteigts, A., Flocchini, P., Mans, B., Santoro, N.: Measuring temporal lags in delay-tolerant networks. IEEE Trans. Comput. 63(2), 397–410 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Casteigts, A., Flocchini, P., Mans, B., Santoro, N.: Shortest, fastest, and foremost broadcast in dynamic networks. Int. J. Found. Comput. Sci. 26(4), 499–522 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Casteigts, A., Klasing, R., Neggaz, Y.M., Peters, J.G.: Efficiently testing \(T\)-interval connectivity in dynamic graphs. In: Paschos, V.T., Widmayer, P. (eds.) CIAC 2015. LNCS, vol. 9079, pp. 89–100. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-18173-8_6 CrossRefGoogle Scholar
  13. 13.
    Casteigts, A., Klasing, R., Neggaz, Y.M., Peters, J.G.: Calcul de Paramètres Minimaux dans les Graphes Dynamiques. In: 19èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (ALGOTEL) (2017)Google Scholar
  14. 14.
    Dubois, S., Kaaouachi, M.-H., Petit, F.: Enabling minimal dominating set in highly dynamic distributed systems. In: Pelc, A., Schwarzmann, A.A. (eds.) SSS 2015. LNCS, vol. 9212, pp. 51–66. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-21741-3_4 CrossRefGoogle Scholar
  15. 15.
    Flocchini, P., Mans, B., Santoro, N.: On the exploration of time-varying networks. Theor. Comput. Sci. 469, 53–68 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Gibbons, A., Rytter, W.: Efficient Parallel Algorithms. Cambridge University Press, Cambridge (1988)zbMATHGoogle Scholar
  17. 17.
    Godard, E., Mazauric, D.: Computing the dynamic diameter of non-deterministic dynamic networks is hard. In: Gao, J., Efrat, A., Fekete, S.P., Zhang, Y. (eds.) ALGOSENSORS 2014. LNCS, vol. 8847, pp. 88–102. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46018-4_6 Google Scholar
  18. 18.
    Jain, S., Fall, K., Patra, R.: Routing in a delay tolerant network. In: Proceedings of SIGCOMM, pp. 145–158 (2004)Google Scholar
  19. 19.
    JáJá, J.: An Introduction to Parallel Algorithms. Addison-Wesley, Boston (1992)zbMATHGoogle Scholar
  20. 20.
    Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: Proceedings of STOC, pp. 513–522. ACM (2010)Google Scholar
  21. 21.
    O’Dell, R., Wattenhofer, R.: Information dissemination in highly dynamic graphs. In: Proceedings of DIALM-POMC, pp. 104–110. ACM (2005)Google Scholar
  22. 22.
    Raynal, M., Stainer, J., Cao, J., Wu, W.: A simple broadcast algorithm for recurrent dynamic systems. In: 2014 IEEE 28th International Conference on Advanced Information Networking and Applications (AINA), pp. 933–939. IEEE (2014)Google Scholar
  23. 23.
    Viard, T., Latapy, M., Magnien, C.: Computing maximal cliques in link streams. Theor. Comput. Sci. 609, 245–252 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Whitbeck, J., Dias de Amorim, M., Conan, V., Guillaume, J.L.: Temporal reachability graphs. In: Proceedings of MOBICOM, pp. 377–388. ACM (2012)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LaBRI, CNRS, University of BordeauxTalenceFrance
  2. 2.IRIT - SMAC TeamUniversity of ToulouseToulouseFrance
  3. 3.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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