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 ∈ [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-, 1992] remains robust in the noisy model while the diameter-linear algorithm of , 2007 does not. We give a modified version of the algorithm of , 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, broadcasting Ω(1 log n log log n) and Ω(1 log n) messages per round, respectively. We next investigate the extent to which (network) coding improves throughput in noisy radio networks. In particular, we study the coding cap -- the ratio of the throughput of coding to that of routing -- in noisy radio networks. We address the previously perplexing result of 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 Θ(log(n)) gap -- provided receiver faults are introduced. However, we show that sender faults have little effect on throughput. In particular, 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 , 2014 carry over to noisy radio networks with sender faults as well. As a result, if sender faults are introduced then there exist topologies for which there is a Θ(log log n) gap, but the worst case throughput across all topologies is Θ(1 log n) for both coding and routing.
Another model that captures unreliability in radio networks is the model @cite_14 @cite_3 @cite_26 @cite_11 @cite_10 . In this graph-based model, there is a static set of edges that form the network graph @math as well as an additional graph @math which consists of edges that may or may not be present in each round, as chosen by an adversary. While an excellent way to capture an environment where some links are reliable and others are not, the dual graph model fails to model random noise.
@cite_14 @cite_26 @cite_3 @cite_10 @cite_11
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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 + log2 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(log2 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. Practitioners agree that unreliable links, which sometimes deliver messages and sometime do not, are an important characteristic of wireless networks. In contrast, most theoretical models of radio networks fix a static set of links and assume that these links are reliable. This gap between theory and practice motivates us to investigate how unreliable links affect theoretical bounds on broadcast in radio networks. To that end we consider a model that includes two types of links: reliable links, which always deliver messages, and unreliable links, which sometimes fail to deliver messages. We assume that the reliable links induce a connected graph, and that unreliable links are controlled by a worst-case adversary. In the new model we show an Ω(n log n) lower bound on deterministic broadcast in undirected graphs, even when all processes are initially awake and have collision detection, and an Ω(n) lower bound on randomized broadcast in undirected networks of constant diameter. This separates the new model from the classical, reliable model. On the positive side, we give two algorithms that tolerate unreliability: an O(n3 2 √log n)-time deterministic algorithm and a randomized algorithm which terminates in O(n log2 n) rounds with high probability. Packet radio networks are modeled as arbitrary graphs by most researchers. We show that an arbitrary graph is an inaccurate model of the radio networks. This is true because there exists a large class of graphs which will not model the radio networks. Radio networks can be modeled accurately by a restricted class of graphs called the planar point graphs. Since the radio networks can accurately be modeled only by a restricted class of graphs, the NP-completeness results for scheduling using an arbitrary graph as the model, do not correctly reflect the complexity of the problem. We study the broadcast scheduling problem using the restricted class as the model. We show that the problem remains NP-complete even in this restricted domain. We give an O(nlogn) algorithm when all the transceivers are located on a line. We restrict our attention to static allocation in general and TDMA in particular. However, it may be noted that the results presented are also valid for other static allocation schemes. In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In the LOCAL model, this is quite simple: each node broadcasts all of its information in each round, and the number of rounds required will be equal to the diameter of the underlying communication graph. In the GOSSIP model, each node must independently choose a single neighbor to contact, and the lack of global information makes it difficult to make any sort of principled choice. As such, researchers have focused on the uniform gossip algorithm, in which each node independently selects a neighbor uniformly at random. When the graph is well-connected, this works quite well. In a string of beautiful papers, researchers proved a sequence of successively stronger bounds on the number of rounds required in terms of the conductance φ and graph size n, culminating in a bound of O(φ-1 log n). In this paper, we show that a fairly simple modification of the protocol gives an algorithm that solves the information dissemination problem in at most O(D + polylog (n)) rounds in a network of diameter D, with no dependence on the conductance. This is at most an additive polylogarithmic factor from the trivial lower bound of D, which applies even in the LOCAL model. In fact, we prove that something stronger is true: any algorithm that requires T rounds in the LOCAL model can be simulated in O(T + polylog(n)) rounds in the GOSSIP model. We thus prove that these two models of distributed computation are essentially equivalent.