# Transfer-Efficient Face Routing Using the Planar Graphs of Neighbors in High Density WSNs
## 5 Performance Evaluation
### Simulation Results
The ratio of nodes is 0% when all of the deployed nodes send messages sequentially along the face boundary. When the ratio of nodes is 100%, all nodes are able to forward messages directly to  
Figure 12: Transfer time according to ratio of nodes capable of direct transmission (radio range: 100 m, deployed nodes: 1500). the remote node. TEFR shows performance similar to GFG or SBFR when the nodes send messages sequentially. In addition, as the number of nodes capable of direct transmission increases, it performs better than GFG and SBFR due to the increased ratio of forwarding a message directly to the remote node and the faster computation time for routing than SBFR. Figure 13 is a graph of the total number of hops from the source to the destination by the number of deployed nodes. With GFG, as the number of deployed nodes increases, the edges on the planar graph become shorter. Therefore, the number of hops to journey from the source to the destination increases. Since SBFR and TEFR send a message directly to the most remote node within radio range, the number of hops rarely changes even if the number of nodes increases in the same radio range. SBFR and TEFR show similar hop counts because the number of hops is not related to computation time when constructing a planar graph. Figure 14 compares the number of hops with a change in radio range. With GFG, even if the node that the message can be directly forwarded to is further away due to the increased radio range, since long edges are removed in planarization and a message is forwarded along short edges, the radio range expansion does not affect the number of hops. In SBFR and TEFR, as the radio range increases, the number of hops decreases because they can transfer a message directly to a node that is further away, which was confirmed by the simulation results. Figure 15 depicts a comparison of the amount of location information to be transmitted as the number of nodes increases within the same radio range. Because GFG receives and uses only the position information of the message transfer node's neighbors, as the number of deployed nodes increases, the number of neighboring nodes increases, and so the amount of the location information to be transmitted gradually increases. With SBFR, since the location information on all nodes within 2-hop range must be transmitted to the message transfer node, the amount of location information to be transmitted sharply increases as the number of nodes increases. In other words, when the average number of neighboring nodes in radio range is \(n\), the message transfer node receives the position information on \(n+n^{2}\) nodes since it receives the location information on \(n\) immediate neighboring nodes and \(n\) neighboring nodes for each of them. With TEFR, since the position information on its neighbors and their planar graph nodes is transmitted to the message transfer node, the amount of position information increases further as the number of nodes increases compared to GFG. However, unlike SBFR, the amount of location information does not increase rapidly because only the information of the nodes after planarization is transmitted. As the number of deployed nodes increases, the number of removed nodes in planarization also increases. Therefore, the amount of location information does not increase sharply even if the number of nodes to be deployed increases. Figure 13: Hop counts according to the number of deployed nodes (radio range: 100 m). Figure 16 shows changes in the amount of location information as radio range increases. With GFG, as the radio range increases, the number of the neighbor increases and the amount of location information to be transferred increases accordingly. With SBFR, as the radio range increases, more neighboring nodes transmit position information because of the much larger number of nodes in 2-hop range. Thus, as the radio range is expanded, the amount of the location information to be transmitted increases rapidly.