Abstract
In this paper we study the problem of building a constant-degree connected dominating set (CCDS), a network structure that can be used as a communication backbone, in the dual graph radio network model (Clementi et al. in J Parallel Distrib Comput 64:89–96, 2004; Kuhn et al. in Proceedings of the international symposium on principles of distributed computing 2009, Distrib Comput 24(3–4):187–206 2011, Proceedings of the international symposium on principles of distributed computing 2010). This model includes two types of links: reliable, which always deliver messages, and unreliable, which sometimes fail to deliver messages. Real networks compensate for this differing quality by deploying low-layer detection protocols to filter unreliable from reliable links. With this in mind, we begin by presenting an algorithm that solves the CCDS problem in the dual graph model under the assumption that every process \(u\) is provided with a local link detector set consisting of every neighbor connected to \(u\) by a reliable link. The algorithm solves the CCDS problem in \(O\left( \frac{\varDelta \log ^2{n}}{b} + \log ^3{n}\right) \) rounds, with high probability, where \(\varDelta \) is the maximum degree in the reliable link graph, \(n\) is the network size, and \(b\) is an upper bound in bits on the message size. The algorithm works by first building a Maximal Independent Set (MIS) in \(\log ^3{n}\) time, and then leveraging the local topology knowledge to efficiently connect nearby MIS processes. A natural follow-up question is whether the link detector must be perfectly reliable to solve the CCDS problem. With this in mind, we first describe an algorithm that builds a CCDS in \(O(\varDelta \)polylog\((n))\) time under the assumption of \(O(1)\) unreliable links included in each link detector set. We then prove this algorithm to be (almost) tight by showing that the possible inclusion of only a single unreliable link in each process’s local link detector set is sufficient to require \(\varOmega (\varDelta )\) rounds to solve the CCDS problem, regardless of message size. We conclude by discussing how to apply our algorithm in the setting where the topology of reliable and unreliable links can change over time.
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Notes
It would be sufficient to only add the listening phase to the first epoch, but since each epoch requires \(\varTheta (\log ^2n)\) rounds anyway, for simplicity, we can afford to add the listening phase to each epoch.
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The authors thank the anonymous reviewers for useful comments and suggestions that helped improve the presentation of this paper.
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A preliminary version of this paper appeared in the Proceedings of the 30th ACM Symposium on Principles of Distributed Computing (PODC), pp. 79–88, 2011.
Keren Censor-Hillel is a Shalon Fellow. Part of this work was done while the author was at MIT and supported by the Simons Postdoctoral Fellows Program.
Seth Gilbert is partially supported by the Singapore MOE AcRF-2 Grant MOE2011-T2-2-042.
Nancy Lynch is supported by AFOSR Award Numbers FA9550-13-1-0042 and FA9550-08-1-0159, and NSF Award Numbers CCF-0726514, CCF-AF-0937274, 0939370-CCF, and CCF-1217506.
Calvin Newport is supported by Mobile Mesh Networks (Ford-MIT Alliance Agreement January 2008).
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Censor-Hillel, K., Gilbert, S., Kuhn, F. et al. Structuring unreliable radio networks. Distrib. Comput. 27, 1–19 (2014). https://doi.org/10.1007/s00446-013-0198-8
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DOI: https://doi.org/10.1007/s00446-013-0198-8