Energy-efficient broadcasting in ad hoc wireless networks

Theoretical Computer Science, 2005

We consider the time of broadcasting in ad hoc radio networks mo eled as undirected graphs. In such networks, every node knows only its ow label and a linear bound on the number of nodes but is unaware of the topo ogy of the network, or even of its own neighborhood. Our aim is to stu to what extent the availability of two important characteristics of a broa casting algorithm influences optimal broadcasting time. These character tics are adaptiveness and randomization. Our contribution is establishi upper and lower bounds on optimal broadcasting time for three classes algorithms: adaptive deterministic, oblivious randomized and oblivious d terministic. In two cases we present tight bounds, and in one case a small g remains. We show that for deterministic adaptive algorithms time Ω(n) is r quired even for n-node networks of constant diameter. This lower bound strongest possible, since linear time algorithms are known, and hence esta lishes optimal time Θ(n) for this class. For oblivious randomized algorithm we show an upper bound O(n · min{D, log n}) and a lower bound Ω(n) optimal expected broadcasting time in n-node networks of diameter D. F nally, for oblivious deterministic algorithms we show matching upper a lower bounds Θ(n · min{D, √ n}) on optimal broadcasting time. Our resu imply that enforcing obliviousness has at least as strong negative impact broadcasting time as enforcing determinism, and that algorithms having bo these features are strictly less efficient than those having only one of them

Lecture Notes in Computer Science, 2002

We study deterministic algorithms for the gossiping problem in ad hoc radio networks under the assumption that each combined message contains at most b(n) single messages or bits of auxiliary information, where b is an integer function and n is the number of nodes in the network. We term such a restricted gossiping problem b(n)-gossiping. We show that √ n-gossiping in an ad hoc radio network on n nodes can be done deterministically in time Õ(n 3/2 ) which asymptotically matches the best known upper bound on the time complexity of unrestricted deterministic gossiping † . Our upper bound on √ n-gossiping is tight up to a poly-logarithmic factor and it implies similarly tight upper bounds on b(n)-gossiping where function b is computable and 1 ≤ b(n) ≤ √ n holds. For symmetric ad hoc radio networks, we show that even 1-gossiping can be done deterministically in time Õ(n 3/2 ). We also demonstrate that O(n t )-gossiping in a symmetric ad hoc radio network on n nodes can be done in time O(n 2-t ). Note that the latter upper bound is o(n 3/2 ) when the size of a combined message is ω(n 1/2 ). Furthermore, by adopting known results on repeated randomized broadcasting in symmetric ad hoc radio networks, we derive a randomized protocol for 1-gossiping in these networks running in time Õ(n) on the average. Finally, we observe that when a collision detection mechanism is available, even deterministic 1-gossiping in symmetric ad hoc radio networks can be performed in time Õ(n). Work of this author is supported in part by EPSRC grants GR/N09855 and GR/R85921. † Notation Õ(f (n)) stands for O(f (n) • log c n), for any constant c > 0.

SIAM Journal on Discrete Mathematics, 2004

We consider radio networks modeled as directed graphs. In ad hoc radio networks, every node knows only its own label and a linear bound on the size of the network but is unaware of the topology of the network or even of its own neighborhood. The fastest currently known deterministic broadcasting algorithm working for arbitrary n-node ad hoc radio networks has running time O(n log 2 n). Our main result is a broadcasting algorithm working in time O(n log n log D) for arbitrary n-node ad hoc radio networks of radius D. The best currently known lower bound on broadcasting time in ad hoc radio networks is Ω(n log D); hence our algorithm is the first to shrink the gap between bounds on broadcasting time in radio networks of arbitrary radius to a logarithmic factor. We also show a broadcasting algorithm working in time O(n log D) for complete layered n-node ad hoc radio networks of radius D. The latter complexity is optimal.

2002

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.

Journal of Parallel and Distributed …, 2004

We study the completion time of broadcast operations on static ad hoc wireless networks in presence of unpredictable and dynamical faults. Concerning oblivious fault-tolerant distributed protocols, we provide an OðDnÞ lower bound where n is the number of nodes of the network and D is the source eccentricity in the fault-free part of the network. Rather surprisingly, this lower bound implies that the simple Round Robin protocol, working in OðDnÞ time, is an optimal fault-tolerant oblivious protocol. Then, we demonstrate that networks of oðn=log nÞ maximum in-degree admit faster oblivious protocols. Indeed, we derive an oblivious protocol having OðD minfn; D log ngÞ completion time on any network of maximum in-degree D: Finally, we address the question whether adaptive protocols can be faster than oblivious ones. We show that the answer is negative at least in the general setting: we indeed prove an OðDnÞ lower bound when D ¼ Yð ffiffi ffi n p Þ: This clearly implies that no (adaptive) protocol can achieve, in general, oðDnÞ completion time.

Principles of Distributed Systems, 2004

A radio network is a collection of transmitter-receiver devices (referred to as nodes). ARB (Acknowledged Radio Broadcasting) means transmitting a message from one special node called source to all the nodes and informing the source about its completion. In our model each node takes a synchronization per round and performs transmission or reception at one round. Each node does not have a collision detection capability and knows only own ID. In [1], it is proved that no ARB algorithm exists in the model without collision detection. In this paper, we show that if n ≥ 2, where n is the number of nodes in the network, we can construct algorithms which solve ARB in O(n) rounds for bidirectional graphs and in O(n 3/2) rounds for strongly connected graphs and solve ARG (Acknowledged Radio Gossiping) in O(n log 3 n) rounds for bidirectional graphs and in O(n 3/2) rounds for strongly connected graphs without collision detection.

Lecture Notes in Computer Science, 2011

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 log 3 n + n log 4 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 log 2 n).

Information Processing Letters, 2008

IEEE Transactions on Wireless Communications, 2000

We present capacity and delay scaling laws for random wireless ad hoc networks under all information dissemination modalities (unicast, multicast, broadcast and anycast) when nodes are endowed with multi-packet reception (MPR) capabilities. Information dissemination modalities are modeled with an (n, m, k)-cast formulation, where n, m, and k denote the number of nodes in the network, the number of destinations for each communication group, and the actual number of communication group members that receives the information (i. e., k ≤ m ≤ n), respectively. We show that Θ (R(n) √ m/k), Θ (1/k), and Θ R 2 (n) bits per second constitute a tight bound for the throughput capacity of random wireless ad hoc networks under the protocol model when m = O R −2 (n) , Ω(k) = R −2 (n) = O(m), and k = Ω R −2 (n) , respectively. R(n) denotes the receiver range which depends on the decoding complexity of the nodes. For the minimum receiver range of Θ log n/n to guarantee network connectivity, a gain of Θ(log n) for (n, m, k)-casting is attained with MPR compared to the capacity attained when receivers can decode at most one transmission at a time in [1]. Furthermore, we derive the capacity-delay tradeoff of (n, m, k)-casting when MPR is used. We show that the use of MPR can lead to both increased network capacity and reduced delays in wireless ad hoc networks.

arXiv (Cornell University), 2015

In this paper, we propose solutions for the energy-efficient broadcasting over cross networks, where N nodes are located on two perpendicular lines. Our solutions consist of an algorithm which finds the optimal range assignment in polynomial time (O(N 12 )), a near-optimal algorithm with linear complexity (O(N )), and a distributed algorithm with complexity O(1). To the best of our knowledge, this is the first study presenting an optimal solution for the minimum-energy broadcasting problem for a 2-D network (with cross configuration). We compare our algorithms with the broadcast incremental power (BIP) algorithm, one of the most commonly used methods for solving this problem with complexity O(N 2 ). We demonstrate that our near-optimal algorithm outperforms BIP, and that the distributed algorithm performs close to it. Moreover, the proposed distributed algorithm can be used for more general two-dimensional networks, where the nodes are located on a grid consisting of perpendicular line-segments. The performance of the proposed near-optimal and distributed algorithms tend to be closer to the optimal solution for larger networks.