Structuring unreliable radio networks

Abstract

In this paper we study the problem of building a connected dominating set with constant degree (CCDS) in the dual graph radio network model [4,9,10]. 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 a local link detector set consisting of every neighbor connected to u by a reliable link. The algorithm solves the CCDS problem in O( ∆ log2 n b + log 3 n) rounds, with high probability, where ∆ 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(∆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 Ω(∆) rounds to solve the CCDS problem, regardless of message size. We con- * Supported by the Simons Postdoctoral Fellows Program. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. PODC '11, June 6-8, 2011, San Jose, California, USA. Copyright 2011 ACM 978-1-4503-0719-2/11/06 ...$10.00.clude by discussing how to apply our algorithm in the setting where the topology of reliable and unreliable links can change over time.

Distributed Deterministic Broadcasting in Wireless Networks of Weak Devices

“…In deterministic ad hoc setting with no local knowledge, the fastest O(n log(n/D))-time algorithm in symmetric networks was developed by Kowalski [20], and almost matching lower bound was given by Kowalski and Pelc [22]. For recent results and references in less related settings we refer the reader to [6,23,5,3,13] There is vast literature on randomized algorithms for broadcasting in graph radio model. Since they are quite efficient, there are very few studies of the problem restricted to geometric setting.…”

Distributed Backbone Structure for Algorithms in the SINR Model of Wireless Networks

“…Communication problems are well-studied in the setting of graph radio model, in which stations are not necessarily deployed in a metric space. Due to limited space and the fact that this research area is not directly related to the core of this work, we refer the reader to the recent literature on deterministic [4,7,8,13,19,20]. and randomized [2,7,19,22] solutions.…”

Distributed Randomized Broadcasting in Wireless Networks under the SINR Model

“…In deterministic ad hoc setting with no local knowledge, the fastest O(n log(n/D))-time algorithm in symmetric networks was developed by Kowalski [12], and almost matching lower bound was given by Kowalski and Pelc [13]. For recent results and references in less related settings we refer the reader to [14,13,15] There is also a vast literature on randomized algorithms for broadcasting in graph radio model [16,13,17]. Since they are quite efficient, there are very few studies of the problem restricted to the geometric setting.…”