## 1 Introduction  
Opportunistic network (OppNet) [1; 2] is a delay-tolerant Ad-hoc network, where the source node communicates with the destination without a complete communication route between them. Therefore, the message application uses the \"opportunities\" created by the movement of nodes to implement the end-to-end data transmission. In the background of big data and 5G networks, traditional face-to-face transmission methods are difficult to meet the communication requirements of large data volume, which implies it is vital for message carriers to select the proper relay nodes to forward messages. In recent years, with the rapid development of novel wireless devices, such as mobile phones, smart watches, Bluetooth earphones or other wearable sensor devices, the message applications in opportunistic social networks [3; 4] may obtain more opportunities to communicate with each other. Moreover, the hot issues of opportunistic networks include routing algorithms [5; 6; 7], mobile models [8; 9], security and cooperation [1; 10], and applications [11; 12]. In [8], an experiment, which anonymously tracked the movements of 700 mobile phone users in a special gathering of Boston metropolitan, shows that the delay-tolerance model is able to perform the effective emergency communication in an important subset of nodes, although the connectivity of the network is strictly dependent on the cooperation of mobile devices and the maximum permissible delay. Moreover, the experimentation on the mobile model also proves that the end-to-end connectivity in opportunistic networks can be implemented by node mobility and the store-carry-forward strategy: nodes carrying data packets use the encounter opportunities created by mobile to forward messages to the relay or destination nodes. However, destination addresses are not always available by the message applications, and this may be a big problem in the data transmission process. In particular, most traditional routing algorithms are more likely to adopt the specific addresses of nodes to implement the messages' delivery decisions; it is difficult for them to overcome this strong limitation. Consequently, Profile-based network models [13; 14] for OppNet proposed that the destination of a message can be multiple nodes or a group of nodes defined by their profiles. These profiles characterize nodes by the method of analyzing and comparing their attributes, such as physical characteristics, places of residence, workplaces or hobbies. In the profile-based network model, messages will be sent to the nodes which belong to a destination profile defined by certain attributes instead of network addresses. Apparently, it is a complex task for the message model to obtain the attribute characteristics of nodes or the state of the network, because the complete connectivity never exists in OppNet. On the one hand, obtaining the state of the network through the broadcasting method is efficient, but it is a huge waste of storage space and computing resources. On the other hand, using the single message to study the attribute characteristics of nodes, which may raise another problem of how to choose an optimal moment between network routing and message forwarding. Fortunately, the optimal stopping theory [15] provides a strategy to select an optimal phase to stop studying the state of the network. Consequently, in the process of exploring the state of the network, messages are able to establish enough and accurate statistics about the attribute characteristics of nodes in the network, and the nodes can make precise message delivery decisions in the next phase. However, in the proposed algorithms for opportunistic networks, the node profile defined by their attributes is rarely taken into consideration. Moreover, there is no effective strategy to identify the node profile. In other words, there are two urgent problems in opportunistic networks: how to compare the attribute characteristics of nodes and how to find the destination profile through the gathered statistics.