Cooperative Energy Spanners: Energy-Efficient Topology Control in Cooperative Ad Hoc Networks Ying Zhu Minsu Huang Siyuan Chen Yu Wang Department of Computer Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA. Abstract—Cooperative communication (CC) allows multiple nodes to simultaneously transmit the same packet to the receiver so that the combined signal at the receiver can be correctly decoded. Since CC can reduce the transmission power and extend the transmission coverage, it has been considered in topology control protocols [1], [2]. However, prior research on topology control with CC only focuses on maintaining the network connectivity, minimizing the transmission power of each node, whereas ignores the energy-efficiency of paths in constructed topologies. This may cause inefficient routes and hurt the overall network performance. In this paper, to address this problem, we introduce a new topology control problem: energy-efficient topology control problem with cooperative communication, and propose two topology control algorithms to build cooperative energy spanners in which the energy efficiency of individual paths are guaranteed. Simulation results confirm the nice performance of the proposed algorithms. I. I NTRODUCTION Topology control have been widely studied and applied in wireless ad hoc networks as one of the key energy saving techniques. In order to save energy and extend lifetime of networks topology control lets each wireless node to select certain subset of neighbors or adjust its transmission power meanwhile maintain network connectivity. Chen and Huang [3] first studied the strongly connected topology control prob- lem, which aims to find a connected topology such that the total energy consumption is minimized. They proved such problem is NP-complete. Several following works [4]–[6] have focused on finding the minimum power assignment so that the induced communication graph has some “good” properties such as disjoint paths, connectivity or fault-tolerance. On the other hand, several localized geometrical structures [7]– [9] have been proposed to be used as underlying network topologies. These geometrical structures are usually kept as few link as possible from the original communication graph and can be easily constructed using location information. Recently, a new class of communication techniques, coop- erative communication (CC) [10], [11], has been introduced to allow single antenna devices to take the advantage of the multiple-input-multiple-output (MIMO) systems. This coop- erative communication explores the broadcast nature of the wireless medium and allows nodes that have received the transmitted signal to cooperatively help relaying data for other nodes. Recent study has shown significant performance gain This work is supported in part by the US National Science Foundation (NSF) under Grant No. CNS-0721666, CNS-0915331, and CNS-1050398, and by Tsinghua National Laboratory for Information Science and Technology (TNList). n v v n-1 v 2 v 1 Fig. 1. Inefficiency of Current Topology Control Methods with CC: Solutions in [1], [2] will remove link  1  to minimize the total energy consumption, thus will lead to an inefficient path from  1 to . of cooperative communication in various wireless network ap- plications: energy efficient routing [12]–[14] and connectivity improvement [15]. The cooperative communication techniques can also be used in topology control. In [1], Cardei et al. first studied the topology control problem under cooperative model (denote by TCC) which aims to obtain a strongly-connected topology with minimum total energy consumption. They first showed that this problem is NP-complete and then proposed two algorithms that start from a connected topology assumed to be the output of a traditional (without using CC) topology control algorithm and reduce the energy consumption using CC model. The first algorithm (DTCC) uses 2-hop neighborhood information of each node to reduce the overall energy consumption within its 2-hop neighborhood without hurting the connectivity under CC model. The second algorithm (ITCC) starts from a minimum transmission power, and iteratively increases its power until all nodes within its 1-hop neighborhood are connected under CC model. Observing that the CC technique can also extend the transmission range and thus link disconnected components. In [2], Yu et al. applied CC model in topology control to improve the network connectivity as well as reduce transmission power. Their algorithm first constructs all candidates of bidirectional links using CC model (called cooperative bridges) which can connect different disconnected components in the communi- cation graph with maximum transmission power. Then they apply a 2-layer MST structure (one MST over the CC links to connect the components, the other is inside each component) to further reduce the energy consumption. Even though the proposed solutions in [1], [2] can guarantee the network connectivity and reduce the energy consumption by constructing a sparse structure under CC model, they do not consider the energy efficiency of paths among nodes in