We consider the problem of deterministic broadcasting in radio networks when the nodes have limited knowledge about the topology of the network. We show that for every deterministic broadcasting protocol there exists a network, of radius 2, for which the protocol takes at least @math (n^ 1 4 ) rounds for broadcasting in constant diameter networks. We prove the new lower @math bound for a special family of radius 2 networks. Each network of this family consists of O( n ) components which are connected to each other via only the source node. At the heart of the proof is a novel simulation argument, which essentially says that any arbitrarily complicated strategy of the source node can be simulated by the nodes of the networks, if the source node just transmits partial topological knowledge about some component instead of arbitrary complicated messages. To the best of our knowledge this type of simulation argument is novel and may be useful in further improving the lower bound or may find use in other applications. Keywords: radio networks, deterministic broadcast, lower bound, advice string, simulation, selective families, limited topological knowledge.
@cite_6: 
@cite_0: We consider the problem of waking up n processors of a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to processors and with or without labeling of processors. The main question we answer is: how fast we can wake all the processors up with probability 1 - ? in each of these eight models. In [10] a logarithmic waking algorithm for the strongest set of assumptions is described, while for weaker models only linear and quadratic algorithms were obtained. We prove that in the weakest model (local synchronization, no knowledge of n or labeling) the best waking time is O(n log n). We also show logarithmic or poly-logarithmic waking algorithms for all stronger models, which in some cases gives an exponential improvement over previous results.
@cite_2: We present an improved algorithm to wake up a multi-hop ad-hoc radio network. The goal is to have all the nodes activated, when some of them may wake up spontaneously at arbitrary times and the remaining nodes need to be awoken by the already active ones. The best previously known wake-up algorithm was given by Chrobak, Gasieniec and Kowalski [11], and operated in time O(n5 3 log n), where n is the number of nodes. We give an algorithm with the running time O(n3 2 log n). This also yields better algorithms for other synchronization-type primitives, like leader election and local-clocks synchronization, each with a time performance that differs from that of wake-up by an extra factor of O(log n) only, and improves the best previously known method for the problem by a factor of n1 6. A wake-up algorithm is a schedule of transmissions for each node. It can be represented as a collection of binary sequences. Useful properties of such collections have been abstracted to define a (radio) synchronizer. It has been known that good radio synchronizers exist and previous algorithms [17,11] relied on this. We show how to construct such synchronizers in polynomial time, from suitable constructible expanders. As an application, we obtain a wake-up protocol for a multiple-access channel that activates the network in time O(k2 polylog n), where k is the number of stations that wake up spontaneously, and which can be found in time polynomial in n. We extend the notion of synchronizers to universal synchronizers. We show that there exist universal synchronizers with parameters that guarantee time O(n3 2 log n) of wake-up.
@cite_10: We study the problem of waking up a collection of @math processors connected by a multihop ad hoc ratio network with unknown topology, no access to a global clock, and no collision detection mechanism available. Each node in the network either wakes up spontaneously or gets activated by receiving a wake-up signal from another node. All active nodes transmit the wake-up signals according to a given protocol @math . The running time of @math 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 @math . Our protocol is based on a novel concept of a shift-tolerant selector to which we refer as a (radio) synchronizer. The second protocol is randomized, and its expected running time is @math , where @math is the diameter of the network. Subsequently we show how to employ our wake-up protocols to solve two other communication primitives: leader election and clock synchronization.
@cite_11: 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 n processors of a completely connected broadcast system. Some processors wake up spontaneously, while others have to be woken up. Only awake processors can send messages; a sleeping processor is woken up upon hearing a message. The processors hear a message in a given round if and only if exactly one processor sends a message in that round. Our goal is to wake up all processors as fast as possible in the worst case, assuming an adversary controls which processors wake up and when. We analyze the problem in both the globally synchronous and locally synchronous models with or without the assumption that n is known to the processors. We propose randomized and deterministic algorithms for the problem, as well as lower bounds in some of the cases. These bounds establish a gap between the globally synchronous and locally synchronous models.
In the wake up problem, each node in the network either wakes-up spontaneously or is activated by receiving a wake-up signal from another node. Each active node transmits the wake-up signal according to a given protocol. The running time of a wake-up protocol is the number of steps counted from the first spontaneous wake-up, until all nodes become activated. This problem has been studied under different assumptions in @cite_10 , @cite_2 , @cite_11 , @cite_0 . Asynchronous radio broadcasting has been studied in @cite_6 .