On the construction of maximum residual energy resource broadcast trees with minimum diameter in static ad hoc wireless networks

Each node in a wireless ad hoc network runs on a local energy source that has a limited energy life span. Thus, energy conservation is a critical issue in such networks. In addition, it is in general desirable to construct routes with low hop counts as a route with a high hop count is more likely to be unstable (because the probability that intermediate nodes will move away is higher). In this paper, we address these two issues concurrently with energy conservation as the primary objective and low hop count as the secondary objective. One way of addressing the energy conservation issue is to construct routes that maximize the minimum residual battery capacity available among all nodes in each route. A broadcast tree with all routes satisfying this condition is referred to as a maximum residual energy resource broadcast tree. A maximum residual energy resource broadcast tree with the least diameter is referred to as a minimum diameter maximum residual energy resource broadcast tree and the problem of constructing such a tree is referred to as the minimum diameter maximum residual energy resource broadcast routing problem (MDMRERBRP). We propose an algorithm for MDMRERBRP and prove that MDMRERBRP is optimally solvable in polynomial time using the proposed algorithm. Copyright © 2005 John Wiley & Sons, Ltd.     

Rate-Diversity and Resource-Aware Broadcast and Multicast in Multi-rate Wireless Mesh Networks

This paper focuses on the problem of increasing the traffic capacity (volume of admissible traffic) of broadcast and multicast flows in a wireless mesh network (WMN). We study and suggest routing strategies where the process of constructing the forwarding tree considers three distinct features: (a) the ability of individual mesh nodes to perform link-layer broadcasts at multiple rates, (b) the wireless broadcast advantage, whereby a single broadcast transmission covers multiple neighboring receivers and (c) the residual transmission capacity at a WMN node, subject to intereference-based constraints from existing traffic flows in its neighborhood. Our metric of interest is the total number of broadcast and multicast flows that can be admitted into the network, without resulting in unacceptable degradation in metrics such as packet loss and dissemination latency. Our discrete event simulations show that the broadcast tree construction heuristic which takes both transmission rate and residual bandwidth into account out-performs those that do not. Building on our work on resource-aware broadcast tree construction, we propose a resource-aware multicast tree construction algorithm which exploits the multiple link-layer rates, the wireless broadcast advantage and the amount of resources available. Simulation results show that this algorithm performs better than heuristics based on pruning a broadcast tree or shortest path trees.     

Energy Efficient Broadcast in Wireless Ad hoc Networks with Hitch-hiking

In this paper, we propose a novel concept called Hitch-hiking in order to reduce the energy consumption of broadcast application for wireless networks. Hitch-hiking takes advantage of the physical layer design that facilitates the combining of partial signals to obtain the complete information. The concept of combining partial signals using maximal ratio combiner [15] has been used to improve the reliability of the communication link but has never been exploited to reduce energy consumption in broadcasting over wireless ad hoc networks. We study the advantage of Hitch-hiking for the scenario when the transmission power level of nodes is fixed as well as the scenario when the nodes can adjust their power level. For both scenarios, we show that Hitch-hiking is advantageous and have proposed algorithms to construct broadcast tree with Hitch-hiking taken into consideration. For fixed transmission power case, we propose and analyze a centralized heuristic algorithm called SPWMH (Single Power Wireless Multicast with Hitch-hiking) to construct a broadcast tree with minimum forwarding nodes. For the latter case, we propose a centralized heuristic algorithm called Wireless Multicast with Hitch-hiking (WMH) to construct an energy efficient tree using Hitch-hiking and also present a distributed version of the heuristic. We also evaluate the proposed heuristics through simulation. Simulation results show that Hitch-hiking can reduce the transmission cost of broadcast by as much as 50%. Further, we propose and evaluate a protocol called Power Saving with Broadcast Tree (PSBT) that reduces energy consumption of broadcast by eliminating redundancy in receive operation. Finally, we propose an algorithm that takes advantage of both Hitch-hiking and PSBT in conserving energy. Manish Agarwal is an engineer at Microsoft, Redmond. He received his Masters degree in Electrical and Computer Engineering from University of Massachusetts, Amherst in 2004. He received his undergraduate degree from Indian Institute of Technology, Guwahati. His research interest lies in the field of mobile ad hoc networks. Lixin Gao is an associate professor of Electrical and Computer Engineering at the University of Masschusetts, Amherst. She received her Ph.D. degree in computer science from the University of Massachusettes at Amherst in 1996. Her research interests include multimedia networking and Internet routing. Between May 1999 and January 2000, she was a visiting researcher at AT&T Research Labs and DIMACS. She is an Alfred P. Sloan Fellow and received an NSF CAREER Award in 1999. She is a member of IEEE, ACM, and Sigma Xi. Joon Ho Cho received the B.S. degree (summa cum laude) in electrical engineering from Seoul National University, Seoul, Korea, in 1995 and the M.S.E.E. and Ph.D. degrees in electrical and computer engineering from Purdue University, West Lafayette, IN, in 1997 and 2001, respectively. From 2001 to 2004, he was with the University of Massachusetts at Amherst as an Assistant Professor. Since July 2004, he has been with Pohang University of Science and Technology (POSTECH), Pohang, Korea, where he is presently an Assistant Professor in the Department of Electronic and Electrical Engineering. His research interests include wideband systems, multiuser communications, adaptive signal processing, packet radio networks, and information theory. Dr. Cho is currently an Associate Editor for the IEEE Transactions on Vehicular Technology. Jie Wu is a Professor at Department of Computer Science and Engineering, Florida Atlantic University. He has published over 300 papers in various journal and conference proceedings. His research interests are in the area of mobile computing, routing protocols, fault-tolerant computing, and interconnection networks. Dr. Wu served as a program vice chair for 2000 International Conference on Parallel Processing (ICPP) and a program vice chair for 2001 IEEE International Conference on Distributed Computing Systems (ICDCS). He is a program co-chair for the IEEE 1st International Conference on Mobile Ad-hoc and Sensor Systems (MASS'04). He was a co-guest-editor of a special issue in IEEE Computer on “Ad Hoc Networks”. He also editored several special issues in Journal of Parallel and Distributing Computing (JPDC) and IEEE Transactions on Parallel and Distributed Systems (TPDS). He is the author of the text “Distributed System Design” published by the CRC press. Currently, Dr. Wu serves as an Associate Editor in IEEE Transactions on Parallel and Distributed Systems and three other international journals. Dr. Wu is a recipient of the 1996–97 and 2001–2002 Researcher of the Year Award at Florida Atlantic University. He served as an IEEE Computer Society Distinguished Visitor. Dr. Wu is a Member of ACM and a Senior Member of IEEE.     

Efficient broadcast for wireless ad hoc networks with a realistic physical layer

In this paper, we investigate the low coverage problem of efficient broadcast protocols in wireless ad hoc networks with realistic physical layer models. To minimize energy consumption, efficient protocols aim to select small set of forward nodes and minimum transmission radii. In ideal physical layer model, nodes within forward nodes’ transmission ranges can definitely receive packets; therefore energy efficient protocols can guarantee full coverage for broadcasting. However, in networks with a realistic physical layer, nodes can only receive packets with probability. We present an analytical model to show that the transmission radii used for nodes can be used to establish a tradeoff between minimizing energy consumption and ensuring network coverage. We then propose a mechanism called redundant radius, which involves using two transmission radii, to form a buffer zone that guarantees the availability of logical links in the physical network, one for broadcast tree calculation and the other for actual data transmission. With this mechanism, we extend well-known centralized protocols, BIP and DBIP, and corresponding localized protocols, LBIP and LDBIP. The effectiveness of the proposed scheme in improving network coverage is validated analytically and by simulation.     

Construction of Tree Network with Limited Delivery Latency in Homogeneous Wireless Sensor Networks

In this paper we propose an approximation algorithm, which is called ADCMCST (algorithm with the minimum number of child nodes when the depth is restricted), to construct a tree network for homogeneous wireless sensor network, so as to reduce and balance the payload of each node, and consequently prolong the network lifetime. When the monitoring node obtains the neighbor graph, ADCMCST tries to find a tree topology with a minimum number of child nodes, and then broadcast the topology to every node, and finally a tree network is constructed. Simulation results show that ADCMCST could greatly reduce the topology formation time, and achieve good approximation results; when the compression ratio is less than 70 %, the network lifetime of ADCMCST will be larger than that of energy driven tree construction.     

Towards broadcast redundancy minimization in duty‐cycled wireless sensor networks

Broadcast is an essential operation in wireless sensor networks. Because of the necessity of energy conservation, minimizing the number of transmissions is always a challenging issue in broadcasting scheme design. This paper studies the minimum‐transmission broadcast problem in duty‐cycled wireless sensor networks where each sensor operates under active/dormant cycles. To address the problem, our proposed scheme, Broadcast Redundancy Minimization Scheduling (BRMS), finds a set of forwarding nodes, which minimizes the number of broadcast transmissions. Then, it constructs a forest of sub‐trees based on the relationship between each forwarding node and its corresponding receivers. A broadcast tree is constructed ultimately by connecting all sub‐trees with a minimum number of connectors. Theoretical analysis shows that BRMS obtains a lower approximation ratio as well as time complexity compared with existing schemes. A set of extensive simulations is conducted to evaluate the performance of BRMS. The results reveal that BRMS outperforms others and its solution is close to the lower bound of the problem in terms of the total number of transmissions. Copyright © 2016 John Wiley & Sons, Ltd.     

Energy efficient broadcast routing in static ad hoc wireless networks

In this paper, we discuss energy efficient broadcast in ad hoc wireless networks. The problem of our concern is: given an ad hoc wireless network, find a broadcast tree such that the energy cost of the broadcast tree is minimized. Each node in the network is assumed to have a fixed level of transmission power. We first prove that the problem is NP-hard and propose three heuristic algorithms, namely, shortest path tree heuristic, greedy heuristic, and node weighted Steiner tree-based heuristic, which are centralized algorithms. The approximation ratio of the node weighted Steiner tree-based heuristic is proven to be (1 + 2 ln(n - 1)). Extensive simulations have been conducted and the results have demonstrated the efficiency of the proposed algorithms.     

On the power efficiency of cooperative broadcast in dense wireless networks

A fundamental problem in large scale wireless networks is the energy efficient broadcast of source messages to the whole network. The energy consumption increases as the network size grows, and the optimization of broadcast efficiency becomes more important. In this paper, we study the optimal power allocation problem for cooperative broadcast in dense large-scale networks. In the considered cooperation protocol, a single source initiates the transmission and the rest of the nodes retransmit the source message if they have decoded it reliably. Each node is allocated an-orthogonal channel and the nodes improve their receive signal-to-noise ratio (SNR), hence the energy efficiency, by maximal-ratio combining the receptions of the same packet from different transmitters. We assume that the decoding of the source message is correct as long as the receive SNR exceeds a predetermined threshold. Under the optimal cooperative broadcasting, the transmission order (i.e., the schedule) and the transmission powers of the source and the relays are designed so that every node receives the source message reliably and the total power consumption is minimized. In general, finding the best scheduling in cooperative broadcast is known to be an NP-complete problem. In this paper, we show that the optimal scheduling problem can be solved for dense networks, which we approximate as a continuum of nodes. Under the continuum model, we derive the optimal scheduling and the optimal power density. Furthermore, we propose low-complexity, distributed and power efficient broadcasting schemes and compare their power consumptions with those-of-a traditional noncooperative multihop transmission     

Network correlated data gathering with explicit communication: NP-completeness and algorithms

We consider the problem of correlated data gathering by a network with a sink node and a tree-based communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy-based coding model with explicit communication where coding is simple and the transmission structure optimization is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal.     

Distributed formation of core-based forwarding multicast trees in mobile ad hoc networks

A core-based forwarding multicast tree is a shortest path tree rooted at core node that distributes multicast packets to all group members via the tree after the packets are sent to the core. Traditionally, the bandwidth cost consumed by transmitting a packet from the core via the tree is evaluated by the total weights of all the edges. And, the bandwidth cost is minimized by constructing the multicast tree that has minimum total weights of edges to span all group members. However, when the local broadcast operation is used to multicast a packet, we found that the bandwidth cost is supposed to be evaluated by the total weights of all senders that include the core and all non-leaves. Since the multicast tree with the number of nodes greater than or equal to three has minimum bandwidth cost only when the core is not a leaf, it leads us to find the multicast tree with the minimum number of non-leaves when each sender node has a unit weight. However, no polynomial time approximation scheme can be found for the minimum non-leaf multicast tree problem unless P = NP since the problem is not only NP-hard but also MAX-SNP hard. Thus, a heuristic is proposed to dynamically reduce the number of non-leaves in the multicast tree. Experimental results show that the multicast tree after the execution of our method has smaller number of non-leaves than others in the geometrically distributed network model.     

Clustering routing protocol based on improved PSO algorithm in WSN

Aiming at the problem that the location distribution of cluster head nodes filtered by wireless sensor network clustering routing protocol was unbalanced and the data transmission path of forwarding nodes was unreasonable,which would increase the energy consumption of nodes and shorten the network life cycle,a clustering routing protocol based on improved particle swarm optimization algorithm was proposed.In the process of cluster head election,a new fitness function was established by defining the energy factor and position equalization factor of the node,the better candidate cluster head node was evaluated and selected,the position update speed of the candidate cluster head nodes was adjusted by the optimized update learning factor,the local search and speeded up the convergence of the global search was expanded.According to the distance between the forwarding node and the base station,the single-hop or multi-hop transmission mode was adopted,and a multi-hop method was designed based on the minimum spanning tree to select an optimal multi-hop path for the data transmission of the forwarding node.Simulation results show that the clustering routing protocol based on improved particle swarm optimization algorithm can elect cluster head nodes and forwarding nodes with more balanced energy and location,which shortened the communication distance of the network.The energy consumption of nodes is lower and more balanced,effectively extending the network life cycle.     

Maximum lifetime broadcast communications in cooperative multihop wireless ad hoc networks: Centralized and distributed approaches

We investigate the problem of broadcast routing in energy constrained stationary wireless ad hoc networks with an aim to maximizing the network lifetime measured as the number of successive broadcast sessions that can be supported. We propose an energy-aware spanning tree construction scheme supporting a broadcast request, considering three different signal transmission schemes in the physical layer: (a) point-to-point, (b) point-to-multipoint, and (c) multipoint-to-point. First we present a centralized algorithm that requires global topology information. Next, we extend this to design an approximate distributed algorithm, assuming the availability of k-hop neighborhood information at each node, with k as a parameter. We prove that the centralized scheme has time complexity polynomial in the number of nodes and the distributed scheme has a message complexity that is linear in the number of nodes. Results of numerical experiments demonstrate significant improvement in network lifetime following our centralized scheme compared to existing prominent non-cooperative broadcasting schemes proposed to solve the same lifetime maximization problem in wireless ad hoc networks. Due to lack of global topology information, the distributed solution does not produce as much advantage as the centralized solution. However, we demonstrate that with increasing value of k, the performance of the distributed scheme also improves significantly.     

Hop Constrained Energy-Efficient Broadcasting: Insights from Massively Dense Ad Hoc Networks

We consider source-initiated broadcast session traffic in an ad hoc wireless network operating under a hard constraint on the end-to-end delay between the source and any node in the network. We measure the delay to a given node in the number of hops data travels from the source to that node, and our objective in this paper is to construct an energy-efficient broadcast tree that has a maximum depth Delta, where Delta; represents the end-to-end hop constraint in the network. We characterize the optimal solution to a closely related problem in massively dense networks using a dynamic programming formulation. We prove that the optimal solution can be obtained by an algorithm of polynomial time complexity O(Delta²). The solution to the dynamic program indicates that there is a single optimal policy applicable to all massively dense networks. Elaborating on the insights provided by the structure of the problem in massively dense networks, we design an algorithm for finding a solution to the hop constrained minimum power broadcasting problem in general networks. By extensive simulations, we demonstrate that our proposed optimization-based algorithm generates broadcast trees within 20% of optimality for general dense networks.     

Minimum-Energy Broadcasting in Multi-hop Wireless Networks Using a Single Broadcast Tree

In this paper we address the minimum-energy broadcast problem in multi-hop wireless networks, so that all broadcast requests initiated by different source nodes take place on the same broadcast tree. Our approach differs from the most commonly used one where the determination of the broadcast tree depends on the source node, thus resulting in different tree construction processes for different source nodes. Using a single broadcast tree simplifies considerably the tree maintenance problem and allows scaling to larger networks. We first show that, using the same broadcast tree, the total power consumed for broadcasting from a given source node is at most twice the total power consumed for broadcasting from any other source node. We next develop a polynomial-time approximation algorithm for the construction of a single broadcast tree. The performance analysis of the algorithm indicates that the total power consumed for broadcasting from any source node is within 2H(n−1) from the optimal, where n is the number of nodes in the network and H(n) is the harmonic function. This approximation ratio is close to the best achievable bound in polynomial time. We also provide a useful relation between the minimum-energy broadcast problem and the minimum spanning tree, which shows that a minimum spanning tree may be a good candidate in sparsely connected networks. The performance of our algorithm is also evaluated numerically with simulations. A preliminary version of this work appeared in the Proceedings of WiOpt’04: Modeling and Optimization in Mobile, Ad hoc and Wireless Networks, University of Cambridge, UK, March 2004. Ioannis Papdimitriou was fully supported for this work by the Public Benefit Foundation “ALEXANDER S. ONASSIS”, Athens, Greece. Ioannis Papadimitriou was born in Veria, Greece, in 1976. He received his five year Diploma from the Department of Electronic and Computer Engineering, Technical University of Crete (Chania), Greece, in 1999 (graduating 2nd in class). He is currently a postgraduate student - Ph.D. candidate at the Telecommunications division, Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Greece. His doctoral thesis deals with the design of wireless ad hoc networks. His research interests include broadcast and multicast communication, energy conservation, routing and topology control protocols, MAC layer and QoS issues. During his studies he has been honored with awards and scholarships by the Technical University of Crete, the Hellenic Telecommunications Organization S.A.(OTE S.A.) and Ericsson Hellas S.A. Mr. Papadimitriou has been a member of the Technical Chamber of Greece (TEE) since March 2000, and he has been supported by the Public Benefit Foundation ALEXANDER S. ONASSIS, Athens, Greece, with a scholarship for his doctoral studies from October 2001 to March 2005. Leonidas Georgiadis received the Diploma degree in electrical engineering from Aristotle University, Thessaloniki, Greece, in 1979, and his M.S. and Ph.D. degrees both in electrical engineering from the University of Connecticut, in 1981 and 1986, respectively. From 1981 to 1983 he was with the Greek army. From 1986 to 1987 he was Research Assistant Professor at the University of Virginia, Charlottesville. In 1987 he joined IBM T.J. Watson Research Center, Yorktown Heights, as a Research Staff Member. Since October 1995, he has been with the Telecommunications Department of Aristotle University, Thessaloniki, Greece. His interests are in the area of wireless networks, high speed networks, distributed systems, routing,scheduling, congestion control, modeling and performance analysis. Prof. Georgiadis is a senior member of IEEE Communications Society. In 1992 he received the IBM Outstanding Innovation Award for his work on goal-oriented workload management for multi-class systems.x     

Routing and transmission scheduling for minimizing broadcast delay in multirate wireless mesh networks using directional antennas

Using directional antennas to reduce interference and improve throughput in multihop wireless networks has attracted much attention from the research community in recent years. In this paper, we consider the issue of minimum delay broadcast in multirate wireless mesh networks using directional antennas. We are given a set of mesh routers equipped with directional antennas, one of which is the gateway node and the source of the broadcast. Our objective is to minimize the total transmission delay for all the other nodes to receive a broadcast packet from the source, by determining the set of relay nodes and computing the number and orientations of beams formed by each relay node. We propose a heuristic solution with two steps. Firstly, we construct a broadcast routing tree by defining a new routing metric to select the relay nodes and compute the optimal antenna beams for each relay node. Then, we use a greedy method to make scheduling of concurrent transmissions without causing beam interference. Extensive simulations have demonstrated that our proposed method can reduce the broadcast delay significantly compared with the methods using omnidirectional antennas and single‐rate transmission. In addition, the results also show that our method performs better than the method with fixed antenna beams. Copyright © 2012 John Wiley & Sons, Ltd.     

Minimum-energy all-to-all multicasting in wireless ad hoc networks

A wireless ad hoc network consists of mobile nodes that are powered by batteries. The limited battery lifetime imposes a severe constraint on the network performance, energy conservation in such a network thus is of paramount importance, and energy efficient operations are critical to prolong the lifetime of the network. All-to-all multicasting is one fundamental operation in wireless ad hoc networks, in this paper we focus on the design of energy efficient routing algorithms for this operation. Specifically, we consider the following minimum-energy all-to-all multicasting problem. Given an all-to-all multicast session consisting of a set of terminal nodes in a wireless ad hoc network, where the transmission power of each node is either fixed or adjustable, assume that each terminal node has a message to share with each other, the problem is to build a shared multicast tree spanning all terminal nodes such that the total energy consumption of realizing the all-to-all multicast session by the tree is minimized. We first show that this problem is NP-Complete. We then devise approximation algorithms with guaranteed approximation ratios. We also provide a distributed implementation of the proposed algorithm. We finally conduct experiments by simulations to evaluate the performance of the proposed algorithm. The experimental results demonstrate that the proposed algorithm significantly outperforms all the other known algorithms.     

Reliable video broadcasts via protected Steiner trees

The introduction of the latest generation of ROADMs in the communication long-haul transport networks allows network planners to consider some new cost-effective design alternatives. Specifically, for video broadcast services ROADM wavelength drop-and-continue technology enables simple wavelength connections at each node via a tree-like topology, and the intelligent control plane permits the use of various shared protection schemes (with failure restoration switching times comparable to SONET BLSR). In this article we formulate models for reliable TV/video broadcast. We consider the network topologies based on minimum spanning trees. The objective is to minimize the total network cost while ensuring that the broadcast, originating in one (or two) source node(s), is delivered to a set of destination nodes and the network will tolerate at least one single link failure. The resulting protected tree networks are illustrated, and the cost of protection strategies is analyzed.     

Minimizing Broadcast Latency and Redundancy in Ad Hoc Networks

Network wide broadcasting is a fundamental operation in ad hoc networks. In broadcasting, a source node sends a message to all the other nodes in the network. In this paper, we consider the problem of collision-free broadcasting in ad hoc networks. Our objective is to minimize the latency and the number of transmissions in the broadcast. We show that minimum latency broadcasting is NP-complete for ad hoc networks. We also present a simple distributed collision-free broadcasting algorithm for broadcasting a message. For networks with bounded node transmission ranges, our algorithm simultaneously guarantees that the latency and the number of transmissions are within $O(1)$ times their respective optimal values. Our algorithm and analysis extend to the case when multiple messages are broadcast from multiple sources. Experimental studies indicate that our algorithms perform much better in practice than the analytical guarantees provided for the worst case.      

R-Code: Network coding-based reliable broadcast in wireless mesh networks

Broadcast is an important communication primitive in wireless mesh networks (WMNs). Applications like network-wide software updates require reliable broadcast to ensure that every node in the network receives the information completely and correctly. With underlying unreliable wireless links, a key challenge in implementing reliable broadcast in WMNs is to achieve 100% information reception rate at every node with high communication efficiency and low latency. Recently, network coding has emerged as a promising coding scheme in terms of communication efficiency especially for one to many communication patterns. In this paper, we put forward R-Code, a network coding-based reliable broadcast protocol. We introduce a guardian–ward relationship between neighboring nodes that effectively distributes the responsibility of reliable information delivery – from the global responsibility of the source to the localized responsibilities of guardians to their corresponding wards. We use a link quality-based minimum spanning tree as a backbone to guide the selection of guardians adaptively and the transmission of coded packets accordingly. Opportunistic overhearing is also utilized to improve the performance of the protocol. Extensive simulation results show that R-Code achieves 100% packet delivery ratio (PDR), while enjoying significantly less transmission overhead and shorter broadcast latency, compared with a state-of-the-art reliable broadcast protocol, AdapCode.     

Energy efficient networking via dynamic relay node selection in wireless networks

Mobile wireless ad hoc networks need to maximize their network lifetime (defined as the time until the first node runs out of energy). In the broadcast network lifetime problem, all nodes are sending broadcast traffic, and one asks for an assignment of transmit powers to nodes, and for sets of relay nodes so that the network lifetime is maximized. The selection of a dynamic relay set consisting of a single node (the ‘master’), can be regarded as a special case, providing lower bounds to the optimal lifetime in the general setting. This paper provides a preliminary analysis of such a ‘dynamic master selection’ algorithm, comparing relaying to direct routing.