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Wake up and join me! An energy-efficient algorithm for maximal matching in radio networks

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Abstract

We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resource. Working in a model where both sending and listening for messages deplete energy, we consider the problem of finding a maximal matching of the nodes in a radio network of arbitrary and unknown topology. We present a distributed randomized algorithm that produces, with high probability, a maximal matching. The maximum energy cost per node is \(O\big ((\log n)(\log \Delta )\big ),\) and the time complexity is \(O(\Delta \log n)\). Here n is any upper bound on the number of nodes, and \(\Delta \) is any upper bound on the maximum degree; n and \(\Delta \) are parameters of our algorithm that we assume are known a priori to all the processors. We note that there exist families of graphs for which our bounds on energy cost and time complexity are simultaneously optimal up to polylog factors, so any significant improvement would need additional assumptions about the network topology. We also consider the related problem of assigning, for each node in the network, a neighbor to back up its data in case of eventual node failure. Here, a key goal is to minimize the maximum load, defined as the number of nodes assigned to a single node. We present an efficient decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog (n) factor bigger that the optimum.

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Notes

  1. We note that this is not a necessary condition. If v sends a message and two of its neighbors w and x both decide to listen, it could still happen that only w receives the message, because some vertex in \(N(x) {\setminus } N(w)\) sends a message at the same time as v, thereby causing a fortuitous collision at x.

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Acknowledgements

The authors would like to thank the anonymous referees of the conference version of this paper for helpful comments and suggestions. The second and third authors were partially supported by NSF Grant CCF-1150281. The fourth author was partially supported by NSF Grant CCF-1815316.

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Authors and Affiliations

  1. Department of Computer Science, Rochester Institute of Technology, Rochester, USA

    Varsha Dani

  2. Department of Computer Science, University of New Mexico, Albuquerque, USA

    Aayush Gupta & Thomas P. Hayes

  3. Computer Science and Engineering, University of Michigan, Ann Arbor, USA

    Seth Pettie

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  1. Varsha Dani
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  2. Aayush Gupta
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  3. Thomas P. Hayes
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  4. Seth Pettie
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Correspondence to Varsha Dani.

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Dani, V., Gupta, A., Hayes, T.P. et al. Wake up and join me! An energy-efficient algorithm for maximal matching in radio networks. Distrib. Comput. 36, 373–384 (2023). https://doi.org/10.1007/s00446-022-00426-w

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  • DOI: https://doi.org/10.1007/s00446-022-00426-w

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