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Distributed Reconfiguration of Maximal Independent Sets

Authors Keren Censor-Hillel, Mikaël Rabie

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Author Details

Keren Censor-Hillel
  • Department of Computer Science, Technion, Israel
Mikaël Rabie
  • IRIF, Université de Paris, France
  • Aalto University, Finland

Funding

  • Censor-Hillel, Keren: This project has received funding from the European Union’s Horizon 2020 Research And Innovation Programe under grant agreement no. 755839.
  • Rabie, Mikaël: This work was supported in part by the Academy of Finland, Grant 285721 and ANR DESCARTES (ref. DS0702-2016).

Acknowledgements

The authors thank Alkida Balliu, Michal Dory, Seri Khoury, Dennis Olivetti, and Jukka Suomela for helpful discussions.

Cite As Get BibTex

Keren Censor-Hillel and Mikaël Rabie. Distributed Reconfiguration of Maximal Independent Sets. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 135:1-135:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICALP.2019.135

Abstract

In this paper, we investigate a distributed maximal independent set (MIS) reconfiguration problem, in which there are two maximal independent sets for which every node is given its membership status, and the nodes need to communicate with their neighbors in order to find a reconfiguration schedule that switches from the first MIS to the second. Such a schedule is a list of independent sets that is restricted by forbidding two neighbors to change their membership status at the same step. In addition, these independent sets should provide some covering guarantee.
We show that obtaining an actual MIS (and even a 3-dominating set) in each intermediate step is impossible. However, we provide efficient solutions when the intermediate sets are only required to be independent and 4-dominating, which is almost always possible, as we fully characterize.
Consequently, our goal is to pin down the tradeoff between the possible length of the schedule and the number of communication rounds. We prove that a constant length schedule can be found in O(MIS+R32) rounds, where MIS is the complexity of finding an MIS in a worst-case graph and R32 is the complexity of finding a (3,2)-ruling set. For bounded degree graphs, this is O(log^*n) rounds and we show that it is necessary. On the other extreme, we show that with a constant number of rounds we can find a linear length schedule.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Distributed algorithms
Keywords
  • distributed graph algorithms
  • reconfiguration
  • maximal independent set

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