Energy-Efficient Broadcasting for Cross Wireless Ad-Hoc Networks

Wireless Networks, 2006

In this paper we study the problem of assigning transmission ranges to the nodes of a static ad hoc wireless network so as to minimize the total power consumed under the constraint that enough power is provided to the nodes to ensure that the network is connected. We focus on the MIN-POWER SYMMETRIC CONNECTIVITY problem, in which the bidirectional links established by the transmission ranges are required to form a connected graph. Implicit in previous work on transmission range assignment under asymmetric connectivity requirements is the proof that MIN-POWER SYMMETRIC CONNECTIVITY is NP-hard and that the MST algorithm has a performance ratio of 2. In this paper we make the following contributions: (1) we show that the related MIN-POWER SYMMETRIC UNICAST problem can be solved efficiently by a shortest-path computation in an appropriately constructed auxiliary graph; (2) we give an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 35-40 nodes in 1 hour; (3) we establish the similarity between MIN-POWER SYMMETRIC CONNECTIVITY and the classic STEINER TREE problem in graphs, and use this similarity to give a polynomial-time approximation scheme with performance ratio approaching 5/3 as well as a more practical approximation algorithm with approximation factor 11/6; and (4) we give the results of a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms. * Preliminary versions of the results in this paper have appeared in .

Proceedings of the …, 2008

The Min Energy Broadcast problem consists in assigning transmission ranges to the nodes of an ad-hoc network in order to guarantee a directed spanning tree from a given source node and, at the same time, to minimize the energy consumption (i.e. the energy cost) yielded by the range assignment. Min Energy Broadcast is known to be NPhard. We consider random-grid networks where nodes are chosen independently at random from the n points of a √ n × √ n square grid in the plane. The probability of the existence of a node at a given point of the grid does depend on that point, that is, the probability distribution can be non-uniform. By using information-theoretic arguments, we prove a lower bound (1 − ǫ) n π on the energy cost of any feasible solution for this problem. Then, we provide an efficient solution of energy cost not larger than 1.1204 n π. Finally, we present a fully-distributed protocol that constructs a broadcast range assignment of energy cost not larger than 8n, thus still yielding constant approximation. The energy load is well balanced and, at the same time, the work complexity (i.e. the energy due to all message transmissions of the protocol) is asymptotically optimal. The completion time of the protocol is only an O(log n) factor slower than the optimum. The approximation quality of our distributed solution is also experimentally evaluated. All bounds hold with probability at least 1 − 1/n Θ(1) .

Theoretical Computer Science, 2003

Given a set N of radio stations located on an Euclidean space, a source station s and an integer h (1 6 h 6 |N | − 1), the minimum bounded-hop broadcast range assignment problem consists in ÿnding a range assignment for N of minimum total power consumption that allows broadcast operations from s to every station in N in at most h hops. The problem is known to be NP-hard on d-dimensional spaces for any d

Lecture Notes in Computer Science, 2009

In this paper we propose an energy-efficient broadcast algorithm for wireless networks for the case where the transmission powers of the nodes are fixed. Our algorithm is based on the multicost approach and selects an optimal energy-efficient set of nodes for broadcasting, taking into account: i) the node residual energies, ii) the transmission powers used by the nodes, and iii) the set of nodes that are covered by a specific schedule. Our algorithm is optimal, in the sense that it can optimize any desired function of the total power consumed by the broadcasting task and the minimum of the current residual energies of the nodes, provided that the optimization function is monotonic in each of these parameters. Our algorithm has non-polynomial complexity, thus, we propose a relaxation producing a near-optimal solution in polynomial time. Using simulations we show that the proposed algorithms outperform other established solutions for energy-aware broadcasting with respect to both energy consumption and network lifetime. Moreover, it is shown that the near-optimal multicost algorithm obtains most of the performance benefits of the optimal multicost algorithm at a smaller computational overhead.

Discrete Applied Mathematics, 2006

Motivated by topology control in ad hoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity). The input consists of a directed complete weighted digraph G = (V , c) (that is, c : V × V → R +). The power of a vertex u in a directed spanning subgraph H is given by p H (u) = max uv∈E(H) c(uv), and corresponds to the energy consumption required for node u to transmit to all nodes v with uv ∈ E(H). The power of H is given by p(H) = u∈V p H (u). Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. Min-Power Bounded-Hops Broadcast is a power assignment problem which has as additional input a positive integer d and a r ∈ V. The output H must be a r-rooted outgoing arborescence of depth at most d. We give an (O(log n), O(log n)) bicriteria approximation algorithm for Min-Power Bounded-Hops Broadcast: that is, our output has depth at most O(d log n) and power at most O(log n) times the optimum solution. For the Euclidean case, when c(u, v) = c(v, u) = u, v (here u, v is the Euclidean distance and is a constant between 2 and 5), the output of our algorithm can be modified to give a O((log n)) approximation ratio. Previous results for Min-Power Bounded-Hops Broadcast are only exact algorithms based on dynamic programming for the case when the nodes lie on the line and c(u, v) = c(v, u) = u, v. Our bicriteria results extend to Min-Power Bounded-Hops Strong Connectivity, where H must have a path of at most d edges in between any two nodes. Previous work for Min-Power Bounded-Hops Strong Connectivity consists only of constant or better approximation for special cases of the Euclidean case.

Journal of Discrete Algorithms, 2017

We study energy-efficient broadcasting in wireless networks of unknown topology (ad hoc). We measure energy efficiency by the maximum number of transmissions ('shots') allowed to any node in the network. In particular, we examine the case in which a bound k is given and a node may transmit at most k times during the broadcasting protocol. Initially, we focus on oblivious algorithms for k-shot broadcasting, that is, algorithms where each node decides whether to transmit or not with no consideration of the transmission history. Our main contributions are (a) a lower bound of Ω(n 2 /k) on the broadcasting time of any oblivious k-shot broadcasting algorithm and (b) an oblivious broadcasting protocol that achieves a matching upper bound, namely O(n 2 /k), for every k ≤ √ n and an upper bound of O(n 3/2) for every k > √ n. We also study the general case of adaptive broadcasting protocols where nodes decide whether to transmit based on all the available information, namely the transmission history known by each. We prove a lower bound of Ω n 1+k k on the broadcasting time of any protocol by introducing the transmission tree construction which generalizes previous approaches.

2010

Quickly finding low-energy multicast routings is vital for a wireless system's energy efficiency. Therefore, key aspects for heuristics for the minimum energy multicast problem (MEMP) are time complexity (measured in the numbers |V | and |A| of networking devices and their possible power assignments, respectively) and deviation from optimum. Following a center-oriented approach, we develop the STSuS and STESuS algorithms (time complexity O(|V | 2 ) and O(|V | 2 log |V |), respectively), and analyze their performance in numerical simulations. They deviate from optimum by only ≈ 11% and ≈ 7.5%, respectively, and thereby outperform the well-known MIP (O(|V | 2 ), ≈ 22% deviation) and many other algorithms significantly.

2008

We consider the problem of energy efficient broadcasting in wireless ad hoc network where nodes have limited energy resources. We investigate the scope of using directional antennas for energy efficient broadcast routing in stationary networks and consider the case where wireless nodes can dynamically adjust their transmission power for each broadcast session. Minimum spanning tree (MST) has an interesting property that the longest edge in the tree is the shortest among all the spanning trees. We construct a broadcast tree using minimum spanning tree and show that use of directional antennas, with fixed orientation and fixed beamwidth, for broadcasting data over this broadcast tree strikes a balance in the energy consumption rate among nodes in the network and hence improves overall lifetime of the network.

Mobile Networks and Applications, 2004

In this paper we address the problem of broadcasting in wireless networks, so that the power consumed by any node is as small as possible. This approach is motivated by the fact that nodes in such networks often use batteries and, hence, it is important to conserve energy individually, so that they remain operational for a long time. We formulate the problem as a lexicographic node power optimization one. The problem is in general NP-complete. We provide an optimal algorithm which runs in polynomial time in certain cases. We also provide a heuristic algorithm whose performance relative to the optimal one is fairly satisfactory. We next show that these algorithms can also be used to solve the problem of broadcasting so that the residual energy of any node after the broadcast process is as large as possible. Finally, we discuss the issues of implementing the above algorithms distributively, as well as their multicast extensions.

Proc. WiOPT

In this paper we address the problem of broadcasting in wireless networks, so that the power consumed by any node is as small as possible. This approach is motivated by the fact that nodes in such networks often use batteries and, hence, it is important to conserve energy individually, so that they remain operational for a long time. We formulate the problem as a lexicographic node power optimization one. The problem is in general NP-complete. We provide an optimal algorithm which runs in polynomial time in certain cases. We also provide a heuristic algorithm whose performance relative to the optimal one is fairly satisfactory. We next show that these algorithms can also be used to solve the problem of broadcasting so that the remaining battery lifetime of any node is as large as possible. Finally, we discuss the issues of implementing the above algorithms distributively, as well as their multicast extensions.