# Combined Sweeping and Jumping Method to Enhance Node Insertion Algorithm for Wi-Fi Sensor Networks
## 3 Numerical Results
As can be seen in Tables 2 and 3, for the circular and donut-shaped service areas, the node insertion algorithm derives a smaller number of serially connected multipolling sequences of sensors both with and without the proposed combined sweeping and jumping method as the number \(l\) of sensors grows in wireless sensor networks. It can be seen that in the case of \(l=1000\), almost a single serially connected multipolling sequence is produced by the node insertion algorithm both with and without the proposed sweeping and jumping method. It also can be seen that for the circular and donut-shaped service areas, the times taken for the node insertion algorithm both with and without the proposed sweeping and jumping method to derive the serially connected multipolling sequences of sensors grow as the number \(l\) of sensors grows in wireless sensor networks. The proposed combined sweeping and jumping method significantly reduces the time taken to produce the near-optimal number of serially connected multipolling sequences for the sensors in wireless sensor networks. When \(l=1000\), the node insertion algorithm with the proposed combined sweeping and jumping method on the average produces the near-optimal solution within 1.6 ms and 2.9 ms in the cases of the circular and donut-shaped service areas, respectively. The results of the stress test for the node insertion algorithm by concentrating the sensors near the boundary of the service area rather than distributing the sensors over the circular service area are explained. Compared to the results of the circular service area, the results of the donut-shaped service area show that the node insertion algorithm without the combined sweeping and jumping method on the average produces about a 13.2% smaller number of serially connected multipolling sequences within about a 9.5% larger amount of time. Furthermore, compared to the results of the circular service area, the results of the donut-shaped service area show that the node insertion algorithm with the combined sweeping and jumping method on the average produces about an 11.1% smaller number of serially connected multipolling sequences within about a 5.9% larger amount of time. In can be seen that even though the node insertion algorithm with the combined sweeping and jumping method takes slightly more time to produce the pseudo-optimal number of serially connected multipolling sequences for the donut-shaped service area than it does for the circular service area, it works fine to produce the pseudo-minimal number of serially connected multipolling sequences. By the node insertion algorithm with the proposed combined sweeping and jumping method, APs can update the near-optimal numbers of serially connected multipolling sequences that cover all the sensors in wireless sensor networks about every 3 or 4 ms, reflecting the connectivity information among sensors in an almost real-time manner. Thanks to the node insertion algorithm with the proposed combined sweeping and jumping  
Figure 3: Circular and donut-shaped service areas. method, the connectivity-based multipolling MAC protocol is able to be applied to wireless sensor networks with an immense number of sensors.