Abstract-Network-assisted Device-to-Device (D2D) communication is a promising technology for improving the performance of proximity-based services. This paper demonstrates how D2D communication can be used to improve the energy-efficiency of cellular networks, leading to a greener system operation and a prolonged battery life of the mobile devices. Assuming a flexible TDD system, we develop optimal mode selection policies for minimizing the energy cost (either from the system or from the device perspective) while guaranteeing a certain rate requirement. The jointly optimal transmit power and time allocation, as well as the optimal mode selection, is found by solving a small convex optimization problem. Special attention is given to the geometrical interpretation of the obtained results. We show that when network energy is the primary concern, D2D mode is preferable in a large portion of the cell. When the device energy consumption is most important, on the other hand, the area where D2D mode is preferable shrinks and becomes close to circular. Finally, we investigate how network parameters affect the range where direct communication is preferred.Index Terms-Network-assisted Device-to-Device, Mode Selection, TDD-LTE, Energy Efficient Communications I. INTRODUCTION During the last decade, the number of mobile subscribers and their traffic demand has increased tremendously, resulting in a larger energy consumption for cellular networks. Furthermore, the battery lifetime of mobile devices has been reduced considerably. Network-assisted Device-to-Device (D2D) communication is a promising technology to improve energy efficiency in future wireless networks: when mobile users in proximity to each other need to exchange data at high rate (e.g. media sharing, gaming, and other proximity-based services [1,2]), direct communication can potentially offload the BS and improve throughput, delay and energy consumption [3,4].A natural question in the context of D2D communication is under which condition two users should communicate through a direct link rather than via the BS. We call this problem the mode selection problem. The optimal mode selection naturally depends on the performance measure that we would like to optimize. For example, the authors in [5] select the transmission mode to maximize user rate in both single-cell and multiple-cell scenarios, while satisfying SINR constraints on active cellular links. In [6] and [7], the authors focus on maximizing the power-efficiency of the network. A joint mode selection and resource allocation problem in a multicell scenario is presented in [8] and shown to be NP-Hard. In [9], the authors address the mode selection problem of