## 4 Proposed Method
### RevAuc Procedure Using D2D Communication  
Compared to the existing method, the proposed method reduces cellular traffic between the server and mobile hosts by utilizing D2D communication. Among mobile hosts that can communicate with a mobile host MH-A by one-hop D2D communication (one-hop neighbors of MH-A), a mobile host volunteers to serve as a REP autonomously if no mobile host has volunteered to serve as a REP among one-hop neighbors of MH-A for the configuration parameter time \({T^{\prime}}_{q}\). A REP sends a Bid Invitations Query message to the server when it volunteers to serve as REP. When it receives bid invitations from the server, it forwards the bid invitations to its one-hop neighbors. Then, it receives bids from its one-hop neighbors. Finally, it evaluates the bids and forwards the bid with the highest evaluation score for each bid invitation to the server (Figure 5a). The REP finishes its role as REP after forwarding the bid to the server. After that, another mobile host will volunteer to serve as a new REP to accommodate the movement of mobile hosts. Design Challenges in Obtaining Data at Almost the Same Location for Almost the Same Reward as in the Existing Method  
Some design challenges arise when REPs are used to execute a RevAuc. In the existing method, all potential bidders can tender their bids to the server. When REPs forward bid invitations and bids between the server and their one-hop neighbors, some potential bidders may not be able to tender their bids if they have not received bid invitations from REPs due to insufficient connectivity to REPs and/or the misbehavior of one or more REPs (Figure 5b). Our goal is to obtain data associated with the same location with the same amount of reward within the same amount of time as in the existing method (i.e., to obtain the same result as in the existing method) with less traffic between the server and mobile hosts than in the existing method. Let \(S_{p}(q)\) denote a set of mobile hosts that receive a bid invitation for the data request \(q\) in the proposed method and let \(S_{e}(q)\) denote a set of mobile hosts that receive a bid invitation for the data request \(q\) in the existing method. \(S_{e}(q)\) is expressed as a set of mobile hosts that exist within circle \(C\) shown in Figure 4. To obtain the same result as in the existing method, a bid invitation for data request \(q\) needs to be delivered to a set of mobile hosts \(S_{p}(q)\) so that \(S_{p}(q)\supseteq S_{e}(q)\) is satisfied (Figures 5a and 6). Figure 5: RevAuc procedure using D2D communication. (i-a) Stimulating mobile hosts at suitable positions to volunteer to serve as REPs  
The system needs REPs that satisfy \(\cup_{i\in S_{R}}G_{i}=S_{T}\), where \(S_{R}\) is a set of REPs, \(G_{i}\) is a set of REP \(i\) and its one-hop neighbors, and \(S_{T}\) is a set of all mobile hosts (Figure 7). If \(\cup_{i\in S_{R}}G_{i}\
eq S_{T}\) (Figure 8), the server cannot send a bid invitation to some mobile hosts and there is a possibility that \(S_{p}(q)\supseteq S_{e}(q)\) is not satisfied. In addition, it is necessary that a mobile host volunteers to serve as a REP for its one-hop neighbors within time \(T_{q}\) and that the server sends a bid invitation to mobile hosts via the REP so that the bid invitation can be delivered to all mobile hosts in \(S_{e}(q)\) within the same amount of time as in the existing method. (i-b) Selection of REPs to which the server sends a bid invitation for a data request  
When the server selects a set of REPs \(R_{q}\) to which it sends a bid invitation for a data request \(q\), it needs to try to ensure that \(S_{p}(q)=\cup_{i\in R_{q}}G_{i}\supseteq S_{e}(q)\) can be satisfied while minimizing \(|R_{q}|\) to reduce cellular traffic between the server and mobile hosts. For this reason, the server needs to select \(R_{q}\) based on the locations of all mobile hosts (i.e., REPs and their one-hop neighbors), as in the existing method, to satisfy \(S_{p}(q)\supseteq S_{e}(q)\).