In this paper we present new randomized and deterministic algorithms for the classical problem of broadcasting in radio networks with unknown topology. We consider directed n-node radio networks with specified eccentricity D (maximum distance from the source node to any other node). In a seminal work on randomized broadcasting, Bar-Yehuda et al. presented an algorithm that for any n-node radio network with eccentricity D completes the broadcasting in O(D log n + log 2 n) time, with high probability. This result is almost optimal, since as it has been shown by Kushilevitz and Mansour and Alon et al., every randomized algorithm requires Ω(D log(n/D)+log 2 n) expected time to complete broadcasting. Our first main result closes the gap between the lower

We establish an O(n log² n) upper bound on the time for deterministic distributed broadcasting in multi-hop radio networks with unknown topology. This nearly matches the known lower bound of n log n). The fastest previously known algorithm for this problem works in time O(n 3=2 ). Using our broadcasting algorithm, we develop an O(n 3=2 log 2 n) algorithm for gossiping in the same network model.

In a multihop wireless network, each node has a transmission radius and is able to send a message to one of its neighbors (one-to-one) or all of its neighbors (one-to-all) that are located within the radius. In a broadcasting task, a source node needs to send the same message to all the nodes in the network. In this paper, we propose to reduce the communication overhead of broadcasting algorithm for one-to-one model by applying the concepts of planar graphs such as RNG (relative neighborhood graphs) and connected dominating sets determined by internal nodes. Regular message exchanges between neighbors, which include location updates or signal strengths, suffice to maintain these structures, and they therefore do not impose additional communication overhead. In internal node based broadcasting, messages are forwarded on the edges that connect two internal nodes, and on edges that connect each non-internal node with its closest internal node. A neighbor elimination scheme is added to the...

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Given a finite set S of points (i.e. the stations of a radio network) on a d-dimensional Euclidean space and a positive integer 1 h jSj \Gamma 1, the Min dd h-Range Assignment problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption, provided that the transmission ranges of the stations ensure the communication beween any pair of stations in at most h hops. Two main issues related to this problem are considered in this paper: the trade-off between the power consumption and the number of hops; the computational complexity of the Min dd h-Range Assignment problem. As for the first question, we provide a lower bound on the minimum power consumption of stations on the plane for constant h. The lower bound is a function of jSj, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound as a function of jSj, h and the maximum distance over all pairs of stations in S (i.e. the d...

This paper studies the differences between two levels of synchronization in a distributed broadcast system (or a multiple access channel). In the globally synchronous model, all processors have access to a global clock. In the locally synchronous model, processors have local clocks ticking at the same rate, but each clock starts individually, when the processor wakes up. We consider the fundamental problem of waking up all of n processors of a completely connected broadcast system. Some processors wake up spontaneously, while others have to be woken up. Only wake processors can...

We consider broadcasting in radio networks: one node of the network knows a message that needs to be learned by all the remaining nodes. We seek distributed deterministic algorithms to perform this task. Radio networks are modeled as directed graphs. They are unknown, in the sense that nodes are not assumed to know their neighbors, nor the size of the network, they are aware only of their individual identifying numbers. If more than one message is delivered to a node in a step then the node cannot hear any of them. Nodes cannot distinguish between such collisions and the case when no messages have been delivered in a step. The fastest previously known deterministic algorithm for deterministic distributed broadcasting in unknown radio networks was presented in [6], it worked in time O(n 11=6 ). We develop three new deterministic distributed algorithms. Algorithm A develops further the ideas of [6] and operates in time O(n 1:77291 ) = O(n 9=5 ), for general networks...

We show that for any radio network there exists a schedule of a broadcast whose time is O(D+log n),whereD is the diameter and n is the number of nodes. (This result implies an optimal broadcast to networks with D n).) We present a centralized randomized polynomial time algorithm that given a network and a source, outputs a schedule for broadcasting the message from the source to the rest of the network.

a wake-up signal from another node. Once a node is We study the problem of waking up a collection of activated, it starts executing its wake-up protocol. This processors connected by a multi-hop ad-hoc ratio network with unknown topology, no access to a global clock, and no collision detection mechanism available. Each node in the network wakes-up spontaneously, or it is activated by receiving a wake-up signal from another node. All active nodes transmit the wake-up signals according to a given protocol. The running time of is the number of steps counted from the first spontaneous wake-up, until all nodes become activated. We provide two protocols for this problem. The first one is a deterministic protocol with running time. Our protocol is based on a novel concept of a rotationtolerant

We consider the problem of distributed deterministic broadcasting in radio networks of unknown topology and size. The network is synchronous. 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. Such messages block each other and node u either hears the noise of interference of messages, enabling it to detect a collision, or does not hear anything at all, depending on the model. We assume that nodes know neither the topology nor the size of the network, nor even their immediate neighborhood. The initial knowledge of every node is limited to its own label. Such networks are called ad hoc multi-hop networks. We study the time of deterministic broadcasting under this scenario. For the model without collision detection, we develop a linear-time broadcasting algorithm for symmetric graphs, which is optimal, and an algorithm for arbitrary n-node graphs, working in time O(n 11=6 ). Next we show that broadcasting with acknowledgement is not possible in this model at all. For the model with collision detection, we develop ecient algorithms for broadcasting and for acknowledged broadcasting in strongly connected graphs. Key words: broadcasting, distributed, deterministic, radio network. Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, 02-097 Warszawa, Poland. E-mail: fchlebus,rytterg@mimuw.edu.pl y Department of Computer Science, The University of Liverpool, Liverpool L69 7ZF, United Kingdom. E-mail: fleszek,A.M.Gibbons,rytterg@csc.liv.ac.uk z Departement d'Informatique, Universite du Quebec a Hull, Hull, Quebec J8X 3X7, Canada. Email: Andrzej Pelc@uqah.uquebec.ca Research supported in part by NSERC grant OGP 0008136. This research was done during this author's stay at The Un...