## 4 Repeal Flooding Boundary
### Finding the Repeal-Flooding Boundary
#### 4.1.3 Finding the Repeal-Flooding Boundary in Practice
A node can now use Equation (12) to establish its repeal-flooding boundary. Notice that while the units on both axes in Figure 5 are given in terms of fractions of \(R_{net}\), the ratio \(\frac{r_{i}}{R_{net}}\) used in the horizontal axis can be easily approximated as \(\frac{r_{i}}{R_{net}}\) in hops. For each new search, \(n_{i}\) will update the value of \(R_{i}\) and \(r_{i}\) in hops using the largest estimated value so far, respectively, which will modify the latest value of the repeal-flooding boundary. Figure 6: Signaling packets from node 10 to each target node, considering different repeal-flooding boundary (FB) values. (**a**) Flooding Boundary = 11; (**b**) Flooding Boundary = 7. Figure 7: Estimating the repeal-flooding boundary. Table 2 shows the computation of \(R_{i}\) and \(r_{i}\) after each resource search for the left case in Figure 7 (where node D seeks node C). In contrast, Table 3 shows the same parameters for the case when node A is seeking node B. As the tables show, the estimate of \(R_{i}\) and \(r_{i}\) is accurate for all nodes due to the long route, but not accurate as a result of the short route. Now, it is just a matter of letting each node use the largest estimated value of either \(R_{i}\) and \(r_{i}\) from the two tables in this example to improve its repeal-flooding boundary accuracy. As Table 4 shows, it takes as few as one long resource search using F&C for all nodes to accurately estimate their repeal-flooding boundary. Figure 8 shows how each of the 500 nodes computed its repeal-flooding boundary after two and five previous resource searches using F&C. The same figures show, as a reference, the optimized repeal-flooding boundary for each node (obtained manually). As can be observed in these figures, while repeal-flooding boundary inaccuracies appear after two resource searches, after five resource searches, the majority of nodes estimated a repeal-flooding boundary value that is within two hops of their optimized value. This behavior demonstrates the ability of F&C to set an accurate repeal-flooding boundary value at each node with minimal signaling cost. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Node** & \(FB_{max}\) & \(FB_{optimized}\) \\ \hline A & 9 & 9 \\ B & 9 & 9 \\ C & 6 & 6 \\ D & 6 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Repeal-flooding boundary estimation keeping the largest value of \(FB_{est}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Node** & **\#RQ** & **\#RP** & **\(R\)** & **\(r\)** & \(FB_{est}\) \\ \hline A & 6 & 8 & 7 & 1 & 5 \\ B & 11 & 8 & 9 & 1 & 6 \\ C & 0 & 3 & 2 & 2 & 1 \\ D & 3 & 0 & 2 & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Repeal-flooding boundary estimation from node D seeking a route to node C. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Node** & **\#RQ** & **\#RP** & **\(R\)** & **\(r\)** & \(FB_{est}\) \\ \hline A & 0 & 16 & 8 & 8 & 9 \\ B & 16 & 0 & 8 & 8 & 9 \\ C & 9 & 7 & 8 & 2 & 6 \\ D & 6 & 10 & 8 & 2 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Repeal-flooding boundary estimation from node A seeking a route to node B.