Abstract
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make only weak assumptions on the communication: every process is infinitely often able to communicate with other processes (not necessarily directly).
Our contribution is threefold. First, we propose a new definition of minimal dominating set suitable for the context of time-varying graphs that seems more relevant than existing ones. Next, we provide a necessary and sufficient topological condition for the existence of a deterministic algorithm for minimal dominating set construction in our settings. Finally, we propose a new measure of time complexity in time-varying graph in order to allow fair comparison between algorithms. Indeed, this measure takes account of communication delays attributable to dynamicity of the graph and not to the algorithms.
This work was performed within the Labex SMART, supported by French state funds managed by the ANR within the “Investissements d’Avenir” programme under reference ANR-11-LABX-65.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anagnostopoulos, A., Kumar, R., Mahdian, M., Upfal, E., Vandin, F.: Algorithms on evolving graphs. In: ITCS, pp. 149–160 (2012)
Awerbuch, B., Even, S.: Efficient and reliable broadcast is achievable in an eventually connected network. In: PODC, pp. 278–281 (1984)
Ferreira, A.: Building a reference combinatorial model for manets. Network 18(5), 24–29 (2004)
Schneider, J., Wattenhofer, R.: Coloring unstructured wireless multi-hop networks. In: PODC, pp. 210–219 (2009)
Xuan, B., Ferreira, A., Jarry, A.: Computing shortest, fastest, and foremost journeys in dynamic networks. IJFCS 14(02), 267–285 (2003)
Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. IJPEDS 27(5), 387–408 (2012)
Whitbeck, J., Dias de Amorim, M., Conan, V., Guillaume, J.L.: Temporal reachability graphs. In: MobiCom, pp. 377–388 (2012)
Schneider, J., Wattenhofer, R.: An optimal maximal independent set algorithm for bounded-independence graphs. Distributed Computing 22(5–6), 349–361 (2010)
Casteigts, A., Mans, B., Mathieson, L.: On the feasibility of maintenance algorithms in dynamic graphs. Technical report, arXiv - abs/1107.2722 (2011)
Casteigts, A., Flocchini, P.: Deterministic algorithms in dynamic networks: Problems, analysis, and algorithmic tools. Technical report, DRDC 2013-020 (2013)
Kuhn, F., Moses, Y., Oshman, R.: Coordinated consensus in dynamic networks. In: PODC, pp. 1–10 (2011)
Kuhn, F., Lynch, N.A., Oshman, R.: Distributed computation in dynamic networks. In: STOC, pp. 513–522 (2010)
Casteigts, A., Flocchini, P., Mans, B., Santoro, N.: Deterministic computations in time-varying graphs: Broadcasting under unstructured mobility. In: ICTCS, pp. 111–124 (2010)
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, Heidelberg (2014)
Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations and Advanced Topics, 2nd edn. John Wiley Interscience (2004)
Braud-Santoni, N., Dubois, S., Kaaouachi, M.H., Petit, F.: A generic framework for impossibility results in time-varying graphs. In: APDCM (to appear, 2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Dubois, S., Kaaouachi, MH., Petit, F. (2015). Enabling Minimal Dominating Set in Highly Dynamic Distributed Systems. In: Pelc, A., Schwarzmann, A. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2015. Lecture Notes in Computer Science(), vol 9212. Springer, Cham. https://doi.org/10.1007/978-3-319-21741-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-21741-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21740-6
Online ISBN: 978-3-319-21741-3
eBook Packages: Computer ScienceComputer Science (R0)