When Should You Wait Before Updating? - Toward a Robustness Refinement

Authors Swan Dubois , Laurent Feuilloley , Franck Petit , Mikaël Rabie

Thumbnail PDF


  • Filesize: 0.66 MB
  • 15 pages

Document Identifiers

Author Details

Swan Dubois
  • Sorbonne Université, CNRS, LIP6, DELYS, Paris, France
Laurent Feuilloley
  • Univ Lyon, CNRS, INSA Lyon, UCBL, LIRIS, UMR5205, Villeurbanne, France
Franck Petit
  • Sorbonne Université, CNRS, LIP6, DELYS, Paris, France
Mikaël Rabie
  • Université Paris Cité, CNRS, IRIF, Paris, France


We thank Nicolas El Maalouly for fruitful discussions about perfect matchings and Dennis Olivetti for pointing out reference [Summer, 1979].

Cite AsGet BibTex

Swan Dubois, Laurent Feuilloley, Franck Petit, and Mikaël Rabie. When Should You Wait Before Updating? - Toward a Robustness Refinement. In 2nd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 257, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Consider a dynamic network and a given distributed problem. At any point in time, there might exist several solutions that are equally good with respect to the problem specification, but that are different from an algorithmic perspective, because some could be easier to update than others when the network changes. In other words, one would prefer to have a solution that is more robust to topological changes in the network; and in this direction the best scenario would be that the solution remains correct despite the dynamic of the network. In [Arnaud Casteigts et al., 2020], the authors introduced a very strong robustness criterion: they required that for any removal of edges that maintain the network connected, the solution remains valid. They focus on the maximal independent set problem, and their approach consists in characterizing the graphs in which there exists a robust solution (the existential problem), or even stronger, where any solution is robust (the universal problem). As the robustness criteria is very demanding, few graphs have a robust solution, and even fewer are such that all of their solutions are robust. In this paper, we ask the following question: Can we have robustness for a larger class of networks, if we bound the number k of edge removals allowed? To answer this question, we consider three classic problems: maximal independent set, minimal dominating set and maximal matching. For the universal problem, the answers for the three cases are surprisingly different. For minimal dominating set, the class does not depend on the number of edges removed. For maximal matching, removing only one edge defines a robust class related to perfect matchings, but for all other bounds k, the class is the same as for an arbitrary number of edge removals. Finally, for maximal independent set, there is a strict hierarchy of classes: the class for the bound k is strictly larger than the class for bound k+1. For the robustness notion of [Arnaud Casteigts et al., 2020], no characterization of the class for the existential problem is known, only a polynomial-time recognition algorithm. We show that the situation is even worse for bounded k: even for k = 1, it is NP-hard to decide whether a graph has a robust maximal independent set.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Discrete mathematics
  • Robustness
  • dynamic network
  • temporal graphs
  • edge removal
  • connectivity
  • footprint
  • packing/covering problems
  • maximal independent set
  • maximal matching
  • minimum dominating set
  • perfect matching
  • NP-hardness


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Nicolas Braud Santoni, Swan Dubois, Mohamed Hamza Kaaouachi, and Franck Petit. A generic framework for impossibility results in time-varying graphs. In IEEE 29nd International Symposium on Parallel and Distributed Processing (IPDPS 2015), 17th Workshop on Advances in Parallel and Distributed Computational Models (APDCM 2015), pages 483-489. IEEE, 2015. Google Scholar
  2. Nicolas Braud-Santoni, Swan Dubois, Mohamed-Hamza Kaaouachi, and Franck Petit. The next 700 impossibility results in time-varying graphs. International Journal of Networking and Computing, 6(1):27-41, 2016. Google Scholar
  3. A. Casteigts and P. Flocchini. Deterministic algorithms in dynamic networks: Problems, analysis, and algorithmic tools. Technical report, Defence Research and Development Canada, 2013-020, 2013. Google Scholar
  4. A. Casteigts, P. Flocchini, W. Quattrociocchi, and N. Santoro. Time-varying graphs and dynamic networks. International Journal of Parallel, Emergent and Distributed Systems, 27(5):387-408, 2012. Google Scholar
  5. Arnaud Casteigts, Timothée Corsini, Hervé Hocquard, and Arnaud Labourel. Robustness of distances and diameter in a fragile network. In 1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022, volume 221 of LIPIcs, pages 9:1-9:16, 2022. URL: http://dx.doi.org/10.4230/LIPIcs.SAND.2022.9.
  6. Arnaud Casteigts, Swan Dubois, Franck Petit, and John Michael Robson. Robustness: A new form of heredity motivated by dynamic networks. Theor. Comput. Sci., 806:429-445, 2020. URL: http://dx.doi.org/10.1016/j.tcs.2019.08.008.
  7. Cornelius Croitoru and Emilian Suditu. Perfect stables in graphs. Inf. Process. Lett., 17(1):53-56, 1983. URL: http://dx.doi.org/10.1016/0020-0190(83)90091-1.
  8. Juho Hirvonen and Jukka Suomela. Distributed algorithms, 2020. Available from: URL: https://jukkasuomela.fi/da2020/da2020.pdf.
  9. David Peleg. Distributed computing: a locality-sensitive approach. SIAM, 2000. Google Scholar
  10. David P Summer. Randomly matchable graphs. Journal of Graph Theory, 3(2):183-186, 1979. URL: http://dx.doi.org/10.1002/jgt.3190030209.
  11. B. Xuan, A. Ferreira, and A. Jarry. Computing shortest, fastest, and foremost journeys in dynamic networks. International Journal of Foundations of Computer Science, 14(02):267-285, 2003. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail