Decision Making Phase. Step 1: Turn the mg-tree into its corresponding ic-tree by deleting the vertices with repeated names. Step 2: Use function VOTE to process root t of each processor’s ic-tree and to obtain the common value VOTE(t). The function VOTE(t)= begin if the α is a leaf then output the value α /* condition 1*/ else begin if the number of value λ0 is 3*(t-r+1)+[(n-1) mod 3] output the value α /* condition 2*/ if the majority value isλi, where 1≦ i ≦t output the value λi-1 /* condition 3*/ if the majority value is the non-λj value, where 0≦ j ≦t, m∈{0,1} output the majority value m /* condition 4*/ if the majority value is not existed output the default value φ /* condition 5*/ end end. The function VOTE only counts the non-value λ0 (excluding the last level of the ic-tree) for all vertexes at the r-th level of an ic-tree, where 1≦ r ≦t +1.
Decision Making Phase. The goal of the decision-making phase is to compute a common agreement value for the BA problem. After the message-exchange phase, each node, except the source node, has its own mg-tree. Each node reorganizes its mg-tree into a corresponding ic-tree. The ic-tree is a tree structure that is used to store received messages without repeated node names (the detailed description of the ic-tree is presented in Appendix III). The VOTE function on each node’s ic-tree from the t+1 level to root s of the ic-tree obtains the agreement value VOTE(s). The agreement value VOTE(s) is transmitted to the return nodes. Conditions 1, 4, and 5 in the VOTE function are similar to the conventional majority vote [11]. Condition 2 is used to remove the influence from a malicious faulty node. Condition 3 is used to remove the influence from a no response node and presents the existence of an absentee. A formal description of the VOTE function is shown in below. FUNCTION VOTE(α) begin if the α is a leaf then output the value α /* condition 1*/ else begin if the number of value δ0 is 3*(t-γ+1)+[(n-1) mod 3] output the value α /* condition 2*/ if the majority value is δi, where 1≦ i ≦ (n -1)/3 output the value δi-1 /* condition 3*/ if the majority value is the non-δj value, where 0≦ j ≦(n -1)/3, m∈{0,1} output the majority value m if the majority value does not exist output the default value φ /* condition 4*/ /* condition 5*/ end end. Moreover, the VOTE function only counts the non-value δ0 (excluding the last level of the ic-tree) for all vertexes at the γ-th level of an ic-tree, where 1≦ γ ≦t+1.
Decision Making Phase. In the decision-making phase, each processor without source processor reorganizes its mg-tree into a corresponding ic-tree. The ic-tree is a tree structure that is used to store the received message without repeated group names (the detailed description of the ic-tree is presented in Appendix B). Then, using function VOTE on the root s of each processor’s ic-tree. The common value VOTE(s) is obtained. The function VOTE only counts the non-value λ0 (excluding the last level of the ic-tree) for all vertexes at the γ-th level of an ic-tree, where 1≤γ≤fg+1. The condition 1, condition 4, and condition 5 in the function VOTE are similar to conventional majority vote [11]. The condition 2 is used to remove the influence of a malicious faulty processor. The condition 3 is used to solve the case of dual failure mode and describes the existence of an absentee. The detail descriptions of function VOTE is shown in Figure 5. Protocol GOAPP (Source processor with initial value vs, where 1≤ s ≤ n) Compute the number of rounds required r: γ= ⎣(g -1)/3⎦+1
Decision Making Phase. In the decision making phase, each fault-free processor turns its mg-tree into a corresponding ic-tree by deleting the vertices with duplicated names. An example ic-tree is illustrated in Figure 6-2(e). Finally, using the function VOTE to root the value s for each processor’s ic-tree (VOTE(s)= (VOTE(s1), VOTE(s2), VOTE(s3), VOTE(s4), VOTE(s5), VOTE(s6), VOTE(s7), VOTE(s8) ) =1), an agreement value 1 can be obtained, as shown in Figure 6(f). We can compare the root s value of fault-free processor in G1 in Figure 6(b), we can find that the root value of the fault-free processors in G1, is replaced by 1. That is, after executing the BA protocol GOAPp, all the fault-free processors can agree on a common value 1. X0 X0 X0 X 0 X0 X0 X0 X0 X0 X 0 0 X X X0 x 0 X0 X 0 X0 X0 X00 X 00 Xxxxx 0 r oot 1 1 s 0 1 1 G1 ' s f a ul t - f r e e pr oc e s s o r s 0 G2 ' s f a ul t - f r e e pr oc e s s o r s 0 G3 ' s f a ul t - f r e e pr oc e s s o r s 1 G5 G4 ' s f a ul t - f r e e pr oc e s s o r s 1 G5 ' s f a ul t - f r e e pr oc e s s o r s 1 G6 ' s f a ul t - f r e e pr oc e s s o r s 1 G7 ' s f a ul t - f r e e pr oc e s s o r s 1 G8 ' s f a ul t - f r e e pr oc e s s o r s 1 VMAJ val ues ( mg- t r ees)
Decision Making Phase. The goal of the decision-making phase is to compute a common agreement value for the BA problem. After the message-exchange phase, each node has its own mg-tree. Each node reorganizes its mg-tree into a corresponding information collecting tree (ic-tree). The ic-tree is a tree structure that is used to store received messages without repeated node names (a detailed description of the ic-tree is presented in section 3.5). Using the VOTEad function on each node’s ic-tree from the level t+1 to root s obtains the agreement value VOTEad(s). The agreement value VOTEad(s) is transmitted to the return nodes. The formal description of the VOTEad function is shown in Figure 3. There are five conditions in the VOTEad function. If the vertex α is a leaf, then there is only one value in the vertex α. Thus, the majority value is the value of vertex α (condition 1). Condition 2 is used to remove the influence from malicious faulty nodes. Condition 3 is used to remove the influence from no response nodes and presents the existence of absentees. Condition 4 is used to get the majority value. Condition 5 happens when there is no majority value. Conditions 1, 4, and 5 in the VOTEad function are similar to the conventional majority vote [12] .
Decision Making Phase. Apply function VOTE to root s of each healthy processor’s ms-tree and decide on VOTE(s). Furthermore, each processor has mobility in the mobile network, and it may immigrate into the network or move away from the network. The procedure of these two cases will be described in the followings:
Decision Making Phase. Step 1: Reorganizing the ms-tree into a corresponding ic-tree. Step 2: Function VOTE is applied to root S of each processor’s ic-tree (The function VOTE does not count the value “λ”). Then the common value VOTE(S) is obtained. Function VOTE(α)
Decision Making Phase. Use function VOTE to process the root s of each processor’s ic-tree, and the Decision Value VOTE(s) is obtained. Function VOTE(α) begin if the α is a leaf then output the value α /* condition 1*/ else begin if the number of value λ0 is 3*( t*-r+1)+[(n-1) mod 3] output the value α /*condition 2*/ if the majority value is λi, where 1≦ i ≦t* output the value λi-1 /*condition 3*/ if the majority value is the non-λj value, where 0≦ j ≦t*, m∈{0,1} output the majority value m /*condition 4*/ if the majority value is not existed output the default value φ /*condition 5*/ end
Decision Making Phase. Step 1: Turn the mg-tree into its corresponding ic-tree by deleting the vertices with repeated names. Step 2: Apply the VOTE function to the root s of each node’s ic-tree and obtain the agreement value VOTE(s). Step 3: Transmit the VOTE(s) to the return nodes if there is any return node in the MANET. Extension-Agreement Phase: (for the return node only) Step 1: Receive other nodes’ VOTE(s) values. Step 2: Apply the VOTE function to the received messages to obtain the agreement value.
Decision Making Phase. Step 1. Reorganizing the mg-tree into a corresponding ic-tree. (The vertices with repeated group names are deleted).
