Synchronous Radio Networks Research Articles

Efficient and competitive broadcast in multi-channel radio networks

Consider a single-hop, multi-channel, synchronous radio network in which a source node needs to disseminate a message to all other n−1 nodes. An adversary called Eve, which captures environmental noise and potentially malicious interference, aims to disrupt this process via jamming. Assume sending, listening, or jamming on one channel for one time slot costs one unit of energy. The question is, if Eve spends T units of energy on jamming, can we devise broadcast algorithms in which each node's cost is o(T)? Previous results show such resource competitive algorithms do exist in the single-channel setting: for large T values, each node can receive the message within O(T) time slots while spending only O˜(T/n) energy.In this work, we devise new broadcast algorithms and show that the existence of multiple channels allows faster message dissemination while preserving resource competitiveness. Specifically, if C channels are available, for large T values, our algorithms guarantee each node's runtime is O(T/C), and each node's energy cost is O˜(T/n). Moreover, our algorithms require minimal prior knowledge and allow Eve to be adaptive. Our technical contributions lie in using “epidemic broadcast” in algorithm design to achieve time efficiency and resource competitiveness, and employing coupling techniques in the analysis to handle the adaptivity of the adversary.We also complement algorithmic results with lower bounds, proving both the time complexity and the energy complexity of our algorithms are optimal or near-optimal. In particular, to obtain the lower bound on resource competitiveness, we first prove a new lower bound showing any multi-channel 1-to-1 communication algorithm succeeding with constant probability incurs expected cost of at least Ω(T); then, via simulation and reduction arguments, we show for the broadcast problem, some node incurs a cost of at least Ω(T/n), even in the multi-channel setting.

On the complexity of neighbourhood learning in radio networks

Consider a synchronous radio network of n stationary nodes represented by an undirected graph with maximum degree Δ. Suppose that each node has a unique ID from {1,…,U}, where U≫n. In the neighbourhood learning task, each node must produce a list of the IDs of its neighbours in the network. We prove new lower bounds on the number of slots needed by certain classes of deterministic algorithms that solve this task. First, we show that O(U)-slot round-robin algorithms are optimal for the class of collision-free algorithms. Then, we consider algorithms where each node fixes its entire transmission schedule at the start. For such algorithms, we prove a Ω(Δ2log⁡Δlog⁡U)-slot lower bound on schedule length that holds in very general models, e.g., when nodes possess collision detectors, messages can be of arbitrary size, and nodes know the schedules being followed by all other nodes. We also prove a similar result for the SINR model of radio networks. To prove these results, we consider a generalization of cover-free families of sets. We also show a separation between the class of fixed-schedule algorithms and the class of algorithms where nodes can choose to leave out some transmissions from their schedule.

Efficient broadcasting in radio networks with long-range interference

We study broadcasting, also known as one-to-all communication, in synchronous radio networks with known topology modeled by undirected (symmetric) graphs, where the interference range of a node is likely exceeding its transmission range. In this model, if two nodes are connected by a transmission edge they can communicate directly. On the other hand, if two nodes are connected by an interference edge they cannot communicate directly and transmission of one node disables recipience of any message at the other node. For a network $$G,$$ we term the smallest integer $$d$$ , s.t., for any interference edge $$e$$ there exists a simple path formed of at most $$d$$ transmission edges connecting the endpoints of $$e$$ as its interference distance $$d_I$$ . In this model the schedule of transmissions is precomputed in advance. It is based on the full knowledge of the size and the topology (including location of transmission and interference edges) of the network. We are interested in the design of fast broadcasting schedules that are energy efficient, i.e., based on a bounded number of transmissions executed at each node. We adopt $$n$$ as the number of nodes, $$D_T$$ is the diameter of the subnetwork induced by the transmission edges, and $$\varDelta $$ refers to the maximum combined degree (formed of transmission and interference edges) of the network. We contribute the following new results: (1) We prove that for networks with the interference distance $$d_I\ge 2$$ any broadcasting schedule requires at least $$D_T+\varOmega (\varDelta \cdot \frac{\log {n}}{\log {\varDelta }})$$ rounds. (2) We provide for networks modeled by bipartite graphs an algorithm that computes $$1$$ -shot (each node transmits at most once) broadcasting schedules of length $$O(\varDelta \cdot \log {n})$$ . (3) The main result of the paper is an algorithm that computes a $$1$$ -shot broadcasting schedule of length at most $$4 \cdot D_T + O(\varDelta \cdot d_I \cdot \log ^4{n})$$ for networks with arbitrary topology. Note that in view of the lower bound from (1) if $$d_I$$ is poly-logarithmic in $$n$$ this broadcast schedule is a poly-logarithmic factor away from the optimal solution.

Modeling radio networks

We describe a modeling framework and collection of foundational composition results for the study of probabilistic packet-level distributed algorithms in synchronous radio networks. Existing results in this setting rely on informal descriptions of the channel behavior and therefore lack easy comparability and are prone to error caused by definition subtleties. Our framework rectifies these issues by providing: (1) a method to precisely describe a radio channel as a probabilistic automaton; (2) a mathematical notion of implementing one channel using another channel, allowing for direct comparisons of channel strengths and a natural decomposition of problems into implementing a more powerful channel and solving the problem on the powerful channel; (3) a mathematical definition of a problem and solving a problem; (4) a pair of composition results that simplify the tasks of proving properties about channel implementation algorithms and combining problems with channel implementations. Our goal is to produce a model streamlined for the needs of the radio network algorithms community.

Distributed broadcast in radio networks of unknown topology

A multi-hop synchronous radio network is said to be unknown if the nodes have no knowledge of the topology. A basic task in radio network is that of broadcasting a message (created by a fixed source node) to all nodes of the network. Typical operations in real-life radio networks is the multi-broadcast that consists in performing a set of r independent broadcasts. The study of broadcast operations on unknown radio network is started by the seminal paper of Bar-Yehuda et al. [J. Comput. System Sci. 45 (1992) 104] and has been the subject of several recent works. In this paper, we study the completion and the termination time of distributed protocols for both the (single) broadcast and the multi-broadcast operations on unknown networks as functions of the number of nodes n, the maximum eccentricity D, the maximum in-degree Δ, and the congestion c of the networks. We establish new connections between these operations and some combinatorial concepts, such as selective families, strongly selective families (also known as superimposed codes), and pairwise r- different families. Such connections, combined with a set of new lower and upper bounds on the size of the above families, allow us to derive new lower bounds and new distributed protocols for the broadcast and multi-broadcast operations. In particular, our upper bounds are almost tight and strongly improve over the previous bounds for a large class of networks.

Deterministic radio broadcasting at low cost

AbstractWe consider distributed deterministic broadcasting in synchronous radio networks. A node receives a message in a given round if and only if exactly one of its neighbors transmits. The source message has to reach all nodes. We assume that nodes do not know the network topology or even their immediate neighborhood. (Such networks are called ad hoc.) We are concerned with two efficiency measures of broadcasting algorithms: their execution time (number of rounds) and their cost (number of transmissions). We focus our study on the execution time of algorithms which have cost close to minimum. We consider two scenarios depending on whether nodes know or do not know global parameters of the network: the number n of nodes and the eccentricity D of the source. Our main contribution is proving tight lower bounds on the time of low‐cost broadcasting which show sharp differences between these scenarios. In each case, we also give broadcasting algorithms whose performance matches these lower bounds. © 2002 Wiley Periodicals, Inc.

Faster broadcasting in unknown radio networks

We study the time of distributed deterministic broadcasting in synchronous radio networks of unknown topology and size. If a node u can be reached from two nodes which send messages in the same round, none of the messages is received by u. We assume that nodes are completely ignorant of the network: they know neither its topology, nor size, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Chlebus et al. [Proc. 11th Annual ACM-SIAM Symp. on Discrete Algorithms, 2000, p. 861] constructed a broadcasting algorithm working in time O(n 11/6) under this total ignorance scenario. We improve this result by showing how to broadcast in time O(n 5/3( logn) 1/3) in the same model.

Multiple Communication in Multihop Radio Networks

Two tasks of communication in a multihop synchronous radio network are considered: Point-to-point communication and broadcast (sending a message to all nodes of a network). Efficient protocols for both problems are presented. Even though the protocols are probabilistic, it is shown how to acknowledge messages deterministically. Let n, D, and $\Delta $ be the number of nodes, the diameter and the maximum degree of our network, respectively. Both protocols require a setup phase in which a BFS tree is constructed. This phase takes $O((n + D\log n)\log \Delta )$ time. After the setup, k point-to-point transmissions require $O((k + D)\log \Delta )$ time on the average. Therefore the network allows a new transmission every $O(\log \Delta )$ time slots. Also, k broadcasts require an average of $O((k + D)\log \Delta \log n)$ time. Hence the average throughput of the network is a broadcast every $O(\log \Delta \log n)$ time slots. Both protocols pipeline the messages along the BFS tree. They are always successful on the graph spanned by the BFS tree. Their probabilistic behavior refers only to the running time. Using the above protocols the ranking problem is solved in $O(n\log n\log \Delta )$ time. The performance analysis of both protocols constitutes a new application of queueing theory.