## 1 Introduction  
In the recent decade, with the popularity of mobile devices and the rapid development of communication technologies, the message exchange without the support of wireless infrastructure has become more and more popular [1]. Opportunistic Mobile Network (OppNet) is a type of challenged network, in which contacts between nodes are intermittent, the links between nodes are constantly changing, and there may never exist the connection from a source node to destination [2, 3]. In OppNets, the nodes can exchange data with each other when they are within mutual wireless transmission range, and the store-carry-forward approach is a data transmission mode for all nodes [4, 5, 6, 7]. In this approach, each node stores data to be sent, then forwards to the encounter nodes [8]. To facilitate such data exchanges, nodes in OppNets have to be in listening state to find the neighboring nodes. Generally speaking, the inter-contact interval is much longer than contact duration [9]. Therefore, most of the energy is consumed in idle listening state during inter-contact intervals. According to the measurement result shown in the architecture for Delay Tolerant Network (DTN) throwboxes [10, 11], 99.5% of the total energy is consumed for contact probing. Thus, it is important to improve efficiency and save energy for contact probing. The duty cycle operation is a quite effective method in energy saving. With the duty cycle operation, the state of node can switch between listening and sleeping. The duty cycle operation can be classified into two categories, synchronous and asynchronous duty cycle operations [12]. The synchronous operation requests that the nodes in the network should keep listening state or sleeping state synchronously, which may cause enormous communication overhead. In contrast, the asynchronous method, which allows the nodes in the network operate independently, is a more viable option. Nevertheless, the duty cycle operation may inevitably lead to the decline of the network performance when the node switch to sleeping state for energy saving. That is because when the node switches to sleeping state, many contacts will be missed, which means the opportunities for exchanging data are lost. Consequently, it is necessary to investigate the impact of duty cycle operations on network performance in the OppNets. Currently, some research work [13; 14] focus on investigating the effect when the working schedule based on the duty cycle operation is randomly selected. Simulations show that the design of the working schedule based on the duty cycle operation has a great impact on the performance of the OppNets. Consequently, it is quite significant to design a proper scheduling mechanism to save energy and improve network performance. In addition, if we have the knowledge of the distribution of the inter-contact time, the contact between nodes will be predicted with high accuracy, which is helpful for energy saving in contact probing. In [15; 16; 17], some statistical researches have been done to analyze the characteristics of contact between nodes in OppNets, and [PERSON] et al. in [17] conducted a detailed analysis of the traces of mobile nodes and achieved the result that the inter-contact intervals are self-similar. Based on the above works, in this paper, we design the energy efficient adaptive scheduling mechanism with the inter-contact interval having self-similarity as the assumption. The adaptive scheduling mechanism uses the mathematical method named _LMMSE_ (Linear Minimum Mean Square Error) [18] to predict the future inter-contact interval based on contact histories, and the nodes' state can be adaptively switched between the listening and sleeping state according to the predicted result. The rest of the paper is structured as follows. In Section 2, we introduce the related work in this research area. Then we briefly describe the network model in Section 3. Section 4 introduces the motivations of our study.