Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks. This paper proposes a novel approach for wireless communication, which embraces collisions rather than avoiding them, over an additive channel. It introduces a coding technique called Bounded-Contention Coding (BCC) that allows collisions to be successfully decoded by the receiving nodes into the original transmissions and whose complexity depends on a bound on the contention among the transmitters. BCC enables deterministic local broadcast in a network with n nodes and at most a transmitters with information of l bits each within O(a log n + al) bits of communication with full-duplex radios, and O((a log n + al)(log n)) bits, with high probability, with half-duplex radios. When combined with random linear network coding, BCC gives global broadcast within O((D + a + log n)(a log n + l)) bits, with high probability. This also holds in dynamic networks that can change arbitrarily over time by a worst-case adversary. When no bound on the contention is given, it is shown how to probabilistically estimate it and obtain global broadcast that is adaptive to the true contention in the network.
In the setting of a wireless network, deterministic global broadcast of a single message was studied in @cite_24 @cite_10 @cite_25 , the best results given being @math and @math , where @math is the diameter of the network. Bar- @cite_15 were the first to study randomized global broadcast algorithms. Kowalski and Pelc @cite_24 and Czumaj and Rytter @cite_25 presented randomized solutions based on selecting sequences, with complexities of @math . These algorithms match lower bounds of @cite_3 @cite_36 but in a model that is weaker than the one addressed in this paper. The algorithms mentioned above are all for global broadcast of one message from a known source. For multiple messages, a deterministic algorithm for @math messages with complexity @math appears in @cite_22 , while randomized global broadcast of multiple messages was studied in @cite_37 @cite_31 @cite_1 . We refer the reader to an excellent survey on broadcasting in radio networks in @cite_12 .
@cite_37 @cite_31 @cite_22 @cite_36 @cite_1 @cite_3 @cite_24 @cite_15 @cite_10 @cite_25 @cite_12
2041120044 2161281242 78560857 2095713941 2048565150 2142458954 1983915440 2160268831
Two tasks of communication in a multi-hop 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 ∆ 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 + Dlogn)log∆) time. After the setup, k point-to-point transmissions require O ((k +D)log∆) time on the average. Therefore the network allows a new transmission every O (log∆) time slots. Also, k broadcasts require an average of O ((k +D)log∆logn) time. Hence the average throughput of the network is a broadcast every O(log∆logn) 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 (nlognlog∆) time. The performance analysis of both protocols constitutes a new application of queueing theory. In much of the theoretical literature on wireless algorithms, issues of message dissemination are considered together with issues of contention management. This combination leads to complicated algorithms and analysis, and makes it difficult to extend the work to harder communication problems. In this paper, we present results of a current project aimed at simplifying such algorithms and analysis by decomposing the treatment into two levels, using abstract "MAC layer" specifications to encapsulate the contention management. We use two different abstract MAC layers: the basic one of [14, 15] and a new probabilistic layer. We first present a typical randomized contention-manageent algorithm for a standard graph-based radio network model We show that it implements both abstract MAC layers. We combine this algorithm with greedy algorithms for single-message and multi-message global broadcast and analyze the combination, using both abstract MAC layers as intermediate layers. Using the basic MAC layer, we prove a bound of O(D log(n ∈) log Δ) for the time to deliver a single message everywhere with probability 1 -- ∈, where D is the network diameter, n is the number of nodes, and Δ is the maximum node degree. Using the probabilistic layer, we prove a bound of O((D + log(n ∈)) log Δ), which matches the best previously-known bound for single-message broadcast over the physical network model. For multi-message broadcast, we obtain bounds of O((D + kΔ) log(n ∈) log Δ) using the basic layer and O((D + kΔ log(n ∈)) log Δ) using the probabilistic layer, for the time to deliver a message everywhere in the presence of at most k concurrent messages. We present new distributed deterministic solutions to two communication problems in n-node ad-hoc radio networks: rumor gathering and multi-broadcast. In these problems, some or all nodes of the network initially contain input data called rumors, which have to be learned by other nodes. In rumor gathering, there are k rumors initially distributed arbitrarily among the nodes, and the goal is to collect all the rumors at one node. Our rumor gathering algorithm works in O((k + n) log n) time and our multi-broadcast algorithm works in O(k log3 n + n log4 n) time, for any n-node networks and k rumors (with arbitrary k), which is a substantial improvement over the best previously known deterministic solutions to these problems. As a consequence, we exponentially decrease the gap between upper and lower bounds on the deterministic time complexity of four communication problems: rumor gathering, multi-broadcast, gossiping and routing, in the important case when every node has initially at most one rumor (this is the scenario for gossiping and for the usual formulation of routing). Indeed, for k = O(n), our results simultaneously decrease the complexity gaps for these four problems from polynomial to polylogarithmic in the size of the graph. Moreover, our deterministic gathering algorithm applied for k = O(n) rumors, improves over the best previously known randomized algorithm of time O(k log n + n log2 n). A radio network is a synchronous network of processors that communicate by transmitting messages to their neighbors, where a processor receives a message in a given step if and only if it is silent in this step and precisely one of its neighbors transmits. In this paper we prove the existence of a family of radius-2 networks on n vertices for which any broadcast schedule requires at least Omega((log n log log n)2) rounds of transmissions. This almost matches an upper bound of O(log2 n) rounds for networks of radius 2 proved earlier by Bar-Yehuda, Goldreich, and Itai. We consider distributed broadcasting in radio networks, modeled as undirected graphs, whose nodes have no information on the topology of the network, nor even on their immediate neighborhood. For randomized broadcasting, we give an algorithm working in expected time O(D log(n D) + log2 n) in n-node radio networks of diameter D, which is optimal, as it matches the lower bounds of [1] and Kushilevitz and Mansour [14]. Our algorithm improves the best previously known randomized broadcasting algorithm of Bar-Yehuda, Goldreich and Itai [3], running in expected time O(D log n + log2 n). For deterministic broadcasting, we show the lower bound Ω(n(log n) (log (n D)))) on broadcasting time in n-node radio networks of diameter D. This implies previously known lower bounds of Bar-Yehuda, Goldreich and Itai [3] and Bruschi and Del Pinto [5], and is sharper than any of them in many cases. We also give an algorithm working in time O(n log n), thus shrinking -- for the first time -- the gap between the upper and the lower bound on deterministic broadcasting time to a logarithmic factor. The time-complexity of deterministic and randomized protocols for achieving broadcast (distributing a message from a source to all other nodes) in arbitrary multi-hop radio networks is investigated. In many such networks, communication takes place in synchronous time-slots. A processor receives a message at a certain time-slot if exactly one of its neighbors transmits at that time-slot. We assume no collision-detection mechanism; i.e., it is not always possible to distinguish the case where no neighbor transmits from the case where several neighbors transmit simultaneously. We present a randomized protocol that achieves broadcast in time which is optimal up to a logarithmic factor. In particular, with probability 1 --E, the protocol achieves broadcast within O((D + log n s) ‘log n) time-slots, where n is the number of processors in the network and D its diameter. On the other hand, we prove a linear lower bound on the deterministic time-complexity of broadcast in this model. Namely, we show that any deterministic broadcast protocol requires 8(n) time-slots, even if the network has diameter 3, and n is known to all processors. These two results demonstrate an exponential gap in complexity between randomization and determinism. We consider the problem of broadcasting in an unknown radio network modeled as a directed graph @math , where @math . In unknown networks, every node knows only its own label, while it is unaware of any other parameter of the network, including its neighborhood and even any upper bound on the number of nodes. We show an @math upper bound on the time complexity of deterministic broadcasting. This is an improvement over the currently best upper bound @math for arbitrary networks, thus shrinking exponentially the existing gap between the lower bound @math and the upper bound from @math to @math . 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). Bar- presented an algorithm that for any n-node radio network with eccentricity D completes the broadcasting in O(D log n + log2 n) time, with high probability. This result is almost optimal, since as it has been shown by Kushilevitz and Mansour and , every randomized algorithm requires Ω (D log(n D) + log2 n) expected time to complete broadcasting.Our first main result closes the gap between the lower and upper bound: we describe an optimal randomized broadcasting algorithm whose running time complexity is O(D log (n D + log2 n), with high probability. In particular, we obtain a randomized algorithm that completes broadcasting in any n-node radio network in time O(n), with high probability.The main source of our improvement is a better "selecting sequence" used by the algorithm that brings some stronger property and improves the broadcasting time. Two types of "selecting sequences" are considered: randomized and deterministic ones. The algorithm with a randomized sequence is easier (more intuitive) to analyze but both randomized and deterministic sequences give algorithms of the same asymptotic complexity.