The cost of radio network broadcast for different models of unreliable links

Abstract

We study upper and lower bounds for the global and local broadcast problems in the dual graph model combined with different strength adversaries. The dual graph model is a generalization of the standard graph-based radio network model that includes unreliable links controlled by an adversary. It is motivated by the ubiquity of unreliable links in real wireless networks. Existing results in this model [11,12,3,8] assume an offline adaptive adversary-the strongest type of adversary considered in standard randomized analysis. In this paper, we study the two other standard types of adversaries: online adaptive and oblivious. Our goal is to find a model that captures the unpredictable behavior of real networks while still allowing for efficient broadcast solutions.For the online adaptive dual graph model, we prove a lower bound that shows the existence of constant-diameter graphs in which both types of broadcast require Ω(n/ log n) rounds, for network size n. This result is within log-factors of the (near) tight upper bound for the offline adaptive setting. For the oblivious dual graph model, we describe a global broadcast algorithm that solves the problem in O(D log n + log 2 n) rounds for network diameter D, but prove a lower bound of Ω( √ n/ log n) rounds for local broadcast in this same setting. Finally, under the assumption of geographic constraints on the network graph, we describe a local broadcast algorithm that requires only O(log 2 n log ∆) rounds in the oblivious model, for maximum degree ∆. In addition to the theoretical interest of these results, we argue that the oblivious model (with geographic constraints) captures enough behavior of real networks to render our efficient algorithms useful for real deployments.

Smoothed analysis of dynamic networks

“…Recent interest in studying distributed algorithms in dynamic networks was sparked by Kuhn et al [10]. Many different problems and dynamic network models have since been proposed; e.g., [11,8,6,3,1,5,13,7] (see [9] for a survey). The dynamic random walk lower bound we study was first proposed by Avin et al [2], while the dynamic aggregation lower bound we study was first proposed by Cornejo et al [4].…”

“…We note other techniques have been proposed for exploring the fragility of dynamic network lower bounds. In recent work, for example, Denysyuk et al [5] thwart the exponential random walk lower bound due to [2] by requiring the dynamic graph to include a certain number of static graphs from a well-defined set, while work by Ghaffari et al [7] studies the impact of adversary strength, and Newport [13] studies the impact of graph properties, on lower bounds in the dynamic radio network model.…”

A (Truly) Local Broadcast Layer for Unreliable Radio Networks

“…In this paper, we implement an efficient local broadcast service in the dual graph radio network model [14,16,3,7,10,8], which captures wireless communication over both reliable and unreliable links. In more detail, the dual graph model describes a network with two graphs, one for each type of link.…”

“…More generally speaking, we note that since 2009 [14] we have waged (algorithmic) battle with the complexities introduced by the presence of unpredictable link behavior in the dual graph model-describing upper and lower bounds for a variety of problems [14,16,3,7,10,8]. This paper can be seen as the culmination of this half-decade of effort, in which we integrate what we have learned into a powerful abstraction that renders this realistic but difficult setting tractable to a wider community of algorithm designers.…”

“…To overcome this difficulty, we use as a starting point the general strategy we originally identified in [10]: permute the broadcast probability schedule after the execution begins (and therefore, after the link schedule has already been generated) to regain independence from the topology. The challenge in permuting a broadcast probability schedule, however, is coordinating the nodes sufficiently that they can apply the same permutation.…”