# Energy-Efficient Multi-User Routing in a Software-Defined Multi-Hop Wireless Network
## 2 Related Work  
As a new network architecture model, SDMWN is the background of many research works. One of the most popular topics is centralized routing protocols, which use the global view of the network to develop better routing strategies. In [11], [PERSON] et al. proposed a SDN-based multi-path routing protocol for MWN, which provides a disjoint multi-path for users according to hops and the residual energy of nodes. Compared with the conventional algorithms, it not only reduces the end-to-end delay, but also prolongs the nodes' life time. Besides, in order to solve the problem of load balancing or congestion control, a number of research works [12; 13] proposed some centralized SDN routing protocols in MWN. From [14], we know that the SDN-based traffic aware protocol (SDN-TAP) is an algorithm for monitoring the channel activity of intermediate nodes. Once the potential congestion is found, an alert will be sent to the SDN controller immediately, and the controller will call the load balancing algorithm to find a backup path. In most cases, SDN-TAP handles congestion quickly to reduce the packet loss rate and average end-to-end delay. The work in [15] presented an integrated approach based on the SDN concept to ensure efficient and reliable transmission in flow-aware networks. Even if network failures occur, the SDN controller can still provide solutions to solve congestion quickly based on traffic prediction. More importantly, congestion processing has a clear priority, which can ensure that high-priority transmission tasks get better quality of service. From [16; 17; 18], we know that task allocation for multiple running applications is also an important research field in SDMWN. In [19], [PERSON] and [PERSON] proposed an algorithm to assign tasks on the basis of the location and residual energy of nodes and deployed it in a centralized controller. It not only balanced the energy consumption in the network, but also boosted the success rate of the task arrangement. Therefore, SDMWN is used widely as an emerging network architecture, which provides an excellent experimental background for the research. In terms of routing strategies, due to the increasing demands for network quality of service, QoS routing has become the focus of current network research. According to the underlying routing strategy, the classical algorithms used in unicast QoS routing can be summarized as priority queue, Bellman-Ford, Lagrange relaxation, and so on [20]. Moreover, there are three kinds of QoS metrics for the link value: additive, multiplicative, and concave metrics, which are determined by the research object. For example, calculating the link delay is an additive metric that adds values together. Generally, the calculations of the packet loss rate and bandwidth are multiplicative and concave metrics, respectively. Accordingly, there is a difference in the QoS objectives, and the routing types are different. As far as the main content of this paper is concerned, the transmission request of each user can be regarded as the research on the minimum cost routing path of QoS constraints, i.e., the delay-constrained least-cost (DCLC) routing algorithm. The DCLC algorithm takes energy consumption as the cost and delay as the constraint, which belongs to the additive metric. In [21], it has been proven that this routing problem is NP-hard. Consequently, it is inevitable but worthwhileto sacrifice part of the time for lower costs until an acceptable balance is reached. In order to find a feasible solution in polynomial time, many people have studied this problem. In [22], an optimization method for QoS disjoint multi-path routing that meets the multiple constraints was proposed. Firstly, the analytic hierarchy process (AHP) is used to calculate the weights of multiple constraints, so that the multiple objectives can be converted into a single objective, which is a common method to simplify the multi-constraint problem.