# Structuring Unreliable Radio Networks

In this paper we study the problem of building a connected dominating set with constant degree (CCDS) in the dual graph radio network model. This model includes two types of links: reliable links, which always deliver messages, and unreliable links, 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((Delta log2(n)/b) + log3(n)) rounds, with high probability, where Delta 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 log3(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. To answer this question, we first describe an algorithm that builds a CCDS in O(Delta 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 Omega(Delta) 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.