Lower Bounds for Structuring Unreliable Radio Networks

In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model that now includes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to solve these problems efficiently (i.e., in time polylogarthmic in the network size). We then prove the importance of the assumption that nodes are provided advance knowledge of their reliable neighbors (i.e, neighbors connected by reliable links). Combined, these results answer an open question by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC 2011] are optimal with respect to their dual graph model assumptions. They also provide insight into what properties of an unreliable network enable efficient local computation.Comment: An extended abstract of this work appears in the 2014 proceedings of the International Symposium on Distributed Computing (DISC

The Cost of Global Broadcast in Dynamic Radio Networks

We study the single-message broadcast problem in dynamic radio networks. We show that the time complexity of the problem depends on the amount of stability and connectivity of the dynamic network topology and on the adaptiveness of the adversary providing the dynamic topology. More formally, we model communication using the standard graph-based radio network model. To model the dynamic network, we use a generalization of the synchronous dynamic graph model introduced in [Kuhn et al., STOC 2010]. For integer parameters $T\geq 1$ and $k\geq 1$, we call a dynamic graph $T$-interval $k$-connected if for every interval of $T$ consecutive rounds, there exists a $k$-vertex-connected stable subgraph. Further, for an integer parameter $\tau\geq 0$, we say that the adversary providing the dynamic network is $\tau$-oblivious if for constructing the graph of some round $t$, the adversary has access to all the randomness (and states) of the algorithm up to round $t-\tau$. As our main result, we show that for any $T\geq 1$, any $k\geq 1$, and any $\tau\geq 1$, for a $\tau$-oblivious adversary, there is a distributed algorithm to broadcast a single message in time $O\big(\big(1+\frac{n}{k\cdot\min\left\{\tau,T\right\}}\big)\cdot n\log^3 n\big)$. We further show that even for large interval $k$-connectivity, efficient broadcast is not possible for the usual adaptive adversaries. For a $1$-oblivious adversary, we show that even for any $T\leq (n/k)^{1-\varepsilon}$ (for any constant $\varepsilon>0$) and for any $k\geq 1$, global broadcast in $T$-interval $k$-connected networks requires at least $\Omega(n^2/(k^2\log n))$ time. Further, for a $0$ oblivious adversary, broadcast cannot be solved in $T$-interval $k$-connected networks as long as $T<n-k$.Comment: 17 pages, conference version appeared in OPODIS 201

Broadcasting in Noisy Radio Networks

The widely-studied radio network model [Chlamtac and Kutten, 1985] is a graph-based description that captures the inherent impact of collisions in wireless communication. In this model, the strong assumption is made that node $v$ receives a message from a neighbor if and only if exactly one of its neighbors broadcasts. We relax this assumption by introducing a new noisy radio network model in which random faults occur at senders or receivers. Specifically, for a constant noise parameter $p \in [0,1)$, either every sender has probability $p$ of transmitting noise or every receiver of a single transmission in its neighborhood has probability $p$ of receiving noise. We first study single-message broadcast algorithms in noisy radio networks and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007 does not. We give a modified version of the algorithm of Gasieniec et al., 2007 that is robust to sender and receiver faults, and extend both this modified algorithm and the Decay algorithm to robust multi-message broadcast algorithms. We next investigate the extent to which (network) coding improves throughput in noisy radio networks. We address the previously perplexing result of Alon et al. 2014 that worst case coding throughput is no better than worst case routing throughput up to constants: we show that the worst case throughput performance of coding is, in fact, superior to that of routing -- by a $\Theta(\log(n))$ gap -- provided receiver faults are introduced. However, we show that any coding or routing scheme for the noiseless setting can be transformed to be robust to sender faults with only a constant throughput overhead. These transformations imply that the results of Alon et al., 2014 carry over to noisy radio networks with sender faults.Comment: Principles of Distributed Computing 201

Data Dissemination in Unified Dynamic Wireless Networks

We give efficient algorithms for the fundamental problems of Broadcast and Local Broadcast in dynamic wireless networks. We propose a general model of communication which captures and includes both fading models (like SINR) and graph-based models (such as quasi unit disc graphs, bounded-independence graphs, and protocol model). The only requirement is that the nodes can be embedded in a bounded growth quasi-metric, which is the weakest condition known to ensure distributed operability. Both the nodes and the links of the network are dynamic: nodes can come and go, while the signal strength on links can go up or down. The results improve some of the known bounds even in the static setting, including an optimal algorithm for local broadcasting in the SINR model, which is additionally uniform (independent of network size). An essential component is a procedure for balancing contention, which has potentially wide applicability. The results illustrate the importance of carrier sensing, a stock feature of wireless nodes today, which we encapsulate in primitives to better explore its uses and usefulness.Comment: 28 pages, 2 figure

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

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(Dlog n + log[superscript 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[superscript 2] n logΔ) rounds in the oblivious model, for maximum degree Δ. 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.Ford Motor Company (University Research Program)United States. Air Force Office of Scientific Research (AFOSR Contract No. FA9550- 13-1-0042)National Science Foundation (U.S.) (NSF Award No. CCF-1217506)National Science Foundation (U.S.) (NSF Award No. 0939370-CCF)National Science Foundation (U.S.) (NSF Award No. CCF-AF-0937274)United States. Air Force Office of Scientific Research (AFOSR Contract No. FA9550-08-1-0159)National Science Foundation (U.S.) (NSF Award No. CCF-072651

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 [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(Δ\log[superscript 2] n/b + log[superscript 3] n) rounds, with high probability, where Δ 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[superscript 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(Δpolylog(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(Δ) 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.Simons Foundation. (Postdoctoral Fellows Program)United States. Air Force Office of Scientific Research (Award FA9550-08-1-0159)National Science Foundation (U.S.) (Award CCF-0937274)National Science Foundation (U.S.) (Award CCF-0726514)National Science Foundation (U.S.) (Purdue University) (Science and Technology Center Award 0939370-CCF

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

A (Truly) Local Broadcast Layer for Unreliable Radio Networks

In this paper, we implement an efficient local broadcast service for the dual graph model, which describes communication in a radio network with both reliable and unreliable links. Our local broadcast service offers probabilistic latency guarantees for: (1) message delivery to all reliable neighbors (i.e., neighbors connected by reliable links), and (2) receiving some message when one or more reliable neighbors are broadcasting. This service significantly simplifies the design and analysis of algorithms for the otherwise challenging dual graph model. To this end, we also note that our solution can be interpreted as an implementation of the abstract MAC layer specification---therefore translating the growing corpus of algorithmic results studied on top of this layer to the dual graph model. At the core of our service is a seed agreement routine which enables nodes in the network to achieve "good enough" coordination to overcome the difficulties of unpredictable link behavior. Because this routine has potential application to other problems in this setting, we capture it with a formal specification---simplifying its reuse in other algorithms. Finally, we note that in a break from much work on distributed radio network algorithms, our problem definitions (including error bounds), implementation, and analysis do not depend on global network parameters such as the network size, a goal which required new analysis techniques. We argue that breaking the dependence of these algorithms on global parameters makes more sense and aligns better with the rise of ubiquitous computing, where devices will be increasingly working locally in an otherwise massive network. Our push for locality, in other words, is a contribution independent of the specific radio network model and problem studied here

Weak models of wireless distributed computing Comparison between radio networks and population protocols

This thesis compares weak distributed computing models that are suit- able for extremely limited wireless networks. The comparison is mainly between multiple variations of radio networks and population protocols. The analysis is based on model features, computability and algorithmic complexity. The thesis analyses essential and optional model features, and organizes the models accordingly. It discusses the applicability of results from stronger models to radio network models, including impossibility results, algorithms and their runtime. It analyzes different radio network algorithms for the classical problems in terms of their features, and it discusses their applicability to other radio network models. It reviews the fundamental differences between population protocols and radio networks. Lastly, the comparative analysis summarizes fundamental differences and separating features