Exploiting spontaneous transmissions for broadcasting and leader election in radio networks

We study two fundamental communication primitives: broadcasting and leader election in the classical model of multi-hop radio networks with unknown topology and without collision detection mechanisms. It has been known for almost 20 years that in undirected networks with n nodes and diameter D, randomized broadcasting requires Ω(D log n/D + log2 n) rounds, assuming that uninformed nodes are not allowed to communicate (until they are informed). Only very recently, Haeupler and Wajc (PODC'2016) showed that this bound can be improved for the model with spontaneous transmissions, providing an O(D log n log log n/log D + logO(1) n)-time broadcasting algorithm. In this article, we give a new and faster algorithm that completes broadcasting in O(D log n/log D + logO(1) n) time, succeeding with high probability. This yields the first optimal O(D)-time broadcasting algorithm whenever n is polynomial in D. Furthermore, our approach can be applied to design a new leader election algorithm that matches the performance of our broadcasting algorithm. Previously, all fast randomized leader election algorithms have used broadcasting as a subroutine and their complexity has been asymptotically strictly larger than the complexity of broadcasting. In particular, the fastest previously known randomized leader election algorithm of Ghaffari and Haeupler (SODA'2013) requires O(D log n/D min {log log n, log n/D} + logO(1) n)-time, succeeding with high probability. Our new algorithm again requires O(D log n/log D + logO(1) n) time, also succeeding with high probability

Exploiting spontaneous transmissions for broadcasting and leader election in radio networks

We study two fundamental communication primitives: broadcasting and leader election in the classical model of multi-hop radio networks with unknown topology and without collision detection mechanisms. It has been known for almost 20 years that in undirected networks with n nodes and diameter D, randomized broadcasting requires Omega(D log n/D + log^2 n) rounds in expectation, assuming that uninformed nodes are not allowed to communicate (until they are informed). Only very recently, Haeupler and Wajc (PODC'2016) showed that this bound can be slightly improved for the model with spontaneous transmissions, providing an O(D log n loglog n / log D + log^O(1) n)-time broadcasting algorithm. In this paper, we give a new and faster algorithm that completes broadcasting in O(D log n/log D + log^O(1) n) time, with high probability. This yields the first optimal O(D)-time broadcasting algorithm whenever D is polynomial in n. Furthermore, our approach can be applied to design a new leader election algorithm that matches the performance of our broadcasting algorithm. Previously, all fast randomized leader election algorithms have been using broadcasting as their subroutine and their complexity have been asymptotically strictly bigger than the complexity of broadcasting. In particular, the fastest previously known randomized leader election algorithm of Ghaffari and Haeupler (SODA'2013) requires O(D log n/D min{loglog n, log n/D} + log^O(1) n)-time with high probability. Our new algorithm requires O(D log n / log D + log^O(1) n) time with high probability, and it achieves the optimal O(D) time whenever D is polynomial in n

The Energy Complexity of Broadcast

Energy is often the most constrained resource in networks of battery-powered devices, and as devices become smaller, they spend a larger fraction of their energy on communication (transceiver usage) not computation. As an imperfect proxy for true energy usage, we define energy complexity to be the number of time slots a device transmits/listens; idle time and computation are free. In this paper we investigate the energy complexity of fundamental communication primitives such as broadcast in multi-hop radio networks. We consider models with collision detection (CD) and without (No-CD), as well as both randomized and deterministic algorithms. Some take-away messages from this work include: 1. The energy complexity of broadcast in a multi-hop network is intimately connected to the time complexity of leader election in a single-hop (clique) network. Many existing lower bounds on time complexity immediately transfer to energy complexity. For example, in the CD and No-CD models, we need $\Omega(\log n)$ and $\Omega(\log^2 n)$ energy, respectively. 2. The energy lower bounds above can almost be achieved, given sufficient ($\Omega(n)$) time. In the CD and No-CD models we can solve broadcast using $O(\frac{\log n\log\log n}{\log\log\log n})$ energy and $O(\log^3 n)$ energy, respectively. 3. The complexity measures of Energy and Time are in conflict, and it is an open problem whether both can be minimized simultaneously. We give a tradeoff showing it is possible to be nearly optimal in both measures simultaneously. For any constant $\epsilon>0$, broadcast can be solved in $O(D^{1+\epsilon}\log^{O(1/\epsilon)} n)$ time with $O(\log^{O(1/\epsilon)} n)$ energy, where $D$ is the diameter of the network

Computing in Additive Networks with Bounded-Information Codes

This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is not high contention, as assumed previously, but rather guaranteeing a bounded amount of \emph{information} in each neighborhood per round, a property that we show is achievable using a new random coding technique. Technically, we provide efficient algorithms for fundamental distributed tasks in additive networks, such as solving various symmetry breaking problems, approximating network parameters, and solving an \emph{asymmetry revealing} problem such as computing a maximal input. The key method used is a novel random coding technique that allows a node to successfully decode the received information, as long as it does not contain too many distinct values. We then design our algorithms to produce a limited amount of information in each neighborhood in order to leverage our enriched toolbox for computing in additive networks

Clustering algorithm in initialization of multi-hop wireless sensor networks

In most application scenarios of wireless sensor networks (WSN), sensor nodes are usually deployed randomly and do not have any knowledge about the network environment or even their ID's at the initial stage of their operations. In this paper, we address the clustering problems with a newly deployed multi-hop WSN where most existing clustering algorithms can hardly be used due to the absence of MAC link connections among the nodes. We propose an effective clustering algorithm based on a random contention model without the prior knowledge of the network and the ID's of nodes. Computer simulations have been used to show the effectiveness of the algorithm with a relatively low complexity if compared with existing schemes