Message Exchange Phase. Case σ = 1, run
Message Exchange Phase. Round 1: Transmit vi to all the other processors and receive the initial value vj from processor Pj, for 1≤ j ≤ n. Then, construct the vector Vi = [v1, v2,…, vj,…, vn], 1 ≤ j ≤ n. If a dormant communication medium, say ik, was found, then vk = λ.
Message Exchange Phase. The goal of the message-exchange phase is to collect the messages. In the BA problem, the source node only transmits a message in the first message exchange round. If the source node is a fault-free node, the source node value becomes the agreed initial value. If the source node is a faulty node, the value of the source node does not matter [10]. In the MANET, each node has partial or complete common knowledge of the graphic information for the underlying MANET (this depends on the routing protocols: table-driven, on-demand or hybrid). Each node can transmit message(s) to other nodes in the MANET directly or through intermediate nodes (relay nodes). To prevent message falsification by the relay nodes, the message is encrypted using encryption technology (such like RSA). Faulty relay nodes cannot falsify a message from a sender node to a receiver node. If no message is received from a sender node, the value δ0 is used as the received message. The value δ0 is used to report an absent value. In the message-exchange phase, the number of rounds required γ must be computed, where γ=t+1, and t=(n-1)/3. In the first message exchange round of the message-exchange phase, the source node transmits its initial value vs using encryption technology to all other nodes. Each node then stores the value from the source node in the root s of its mg-tree. The mg-tree is a tree structure that is used to store received messages (a detailed description of the mg-tree is presented in Appendix II). If the initial value vs received from the source node is “δ0,” the value “0” is then used to replace the value “δ0.” After the first message exchange round (γ>1), each node but the source node transmits the values at level γ-1 in its mg-tree using encryption technology to all other nodes. If the value at level γ-1 is δi, the value δi+1 is used as the transmitted value, where 1≤i≤(n-1)/3-1. Each node stores the values received at level γ in its mg-tree.
Message Exchange Phase. At the first round of “message-exchange phase” (r=1), the source processor sends its init ial value vs using encryption technology to all other mobile processors. Hence, each mobile processor in the source mobile processor’ s zone can receive the initial value vs from source mobile processor directly. For other mobile processors which are not in the source mobile processor’ s zone, the source processor can send its initial value by relaying through the gateway processor. Hence, the mobile processors in the different zone can also receive the messages from the source processor. After the first round of message exchange (r>1), each mobile processor without source processor sends the values at level r-1 in its mg -tree [9] to each zone’ s processors, if the value at level r-1 is di, then replace the value di+1 as the transmitted value, where 1≤ i ≤ Zm –1(The value di is used to report the absent value.) At the end of each round, the receiver processor uses function RMAJ (Function RMAJ is shown in Fig. 2) on it received values which from the same zone to get a single value. In addition, each receiver processor stores the received messages and function RMAJ value in its mg -tree.
Message Exchange Phase σ = 1, do: 1) Each gateway processor broadcasts its initial value vi to other gateway processors and itself. 2) Each gateway processor j collects the vi of these initial values from other gateway processors i, 1 ≤ i ≤ N, then construct vector Vj. 3) Run the ic-tree conversion function. 4) Run the early stopping function. σ = 2, do:
Message Exchange Phase. In the first round of message exchange (γ=1), the source processor transmits its initial value to each group’s processors by using RFCp, and then each receiver processor stores the value from RFCp in the roots of its mg-tree. The mg-tree is a tree structure that is used to store the received message (the detailed description of the mg-tree is presented in Appendix A). If the source processor is a dormant faulty processor then replaces the value “0” as the initial value from the source processor. After the first round of message exchange (γ>1), each processor without source processor uses RFCp to transmit the values at level γ-1 in its mg-tree to each group’s processors, if the value at level γ-1 is λi , then replace the value λi+1 as the transmitted value, where 0≤i ≤fg –1(The value λi is used to report the absent value.). At the end of each round, the receiver processor uses function RMAJ (Function RMAJ is shown in Figure 5) on it received VMAJ values which from the same group by RFCp to get a single value. In addition, each receiver processor stores the received messages (VMAJ values) and function RMAJ value in its mg-tree.
Message Exchange Phase. If γ=1 then: 1) The source processor transmits its initial value vs to each group’s processors by using RFCP. 2) Each receiver processor stores the value from RFCP in the root s of its mg-tree. 3) If the initial value vs received from the source processor is “λ0”, then using the value “0” to replace the value “λ0”.
Message Exchange Phase. In the first round of the message exchange phase, the source processor Ps uses RFCp to transmit messages to other processors. The messages sent by the source processor Ps are shown in Figure 6(a). The message stored by each group’s fault-free processors in the first round of the message exchange phase is illustrated in Figure 6-2(b). In the γ-th (γ>1) round of message exchange, except for the source processor, each processor uses RFCp to transmit RMAJ values at the (γ-1)th level in its mg-tree to the others and itself. Then, each receiver processor applies RMAJ to its received messages from RFCp and stores the received messages (VMAJ values) and RMAJ values at the corresponding vertices at level r of its mg-tree. The mg-tree of fault-free processor P1 at the second and third round in the message exchange phase are shown in Figure 6-2(c) and Figure 6-2(d).
Message Exchange Phase. If r = 1, then: 1. The transmitter transmits its initial value vt by RC to the destination processor. 2. Each processor stores the function value from RC in the root t of its mg-tree. 3. If the initial value vt received from the transmitter processor is “λ0”, then using the value “0” to replace the value “λ0”. For r > 1, do: 1. Each processor transmits the values at level r-1 in its mg-tree bye RC to the destination processor, if the value at level r-1 is λi, then replace the value λi+1 as the transmitted value, where 0≦ i ≦t. 2. Each processor stores the function value from RC at level r of its mg-tree.
Message Exchange Phase. If r=1 do:
