# Transfer-Efficient Face Routing Using the Planar Graphs of Neighbors in High Density WSNs
## 2 Related Works  
Early proposals for face routing methods using planar graphs include Greedy Face Greedy (GFG) [20], Compass Routing II [21], Greedy Perimeter Stateless Routing (GPSR) [18], Greedy Other Adaptive Face Routing (GOAFR+) [22], GOAFR++ [23], and Greedy Path Vector Face Routing (GPVFR) [24]. The methods forward a message along a sequence of faces intersecting with line \(\overline{st}\) between the source (s) and the destination (\(t\)). A face change occurs when the edge of a face intersects with line \(\overline{st}\). Messages are delivered based solely on local information and the faces are traversed sequentially. To improve performance, they are able to choose whether to pass through the intersecting edge or not when changing the face or to change how line \(\overline{st}\) is set up and used. That is to say, they improve performance by changing the face after going through or without passing through the intersecting edge. They also enhance efficiency by using the initial setup of line \(\overline{st}\) without changing during the entire routing process, or using a newly set up line \(\overline{st}\) whenever a face is changed. Their performance also depends on the choice of traversal direction change, i.e., clockwise or counterclockwise. In short, early face routing improves performance and efficiency by determining how line \(\overline{st}\) is set, when to change the face, which face to change to, and in which direction to explore the face is. Because they process routing using only local information, not global network information, routing information is not propagated beyond a single hop, thus maintaining locality. This locality means that the size of the routing table is determined according to the density of neighbors regardless of the network's scale. Therefore, it can support scalability by not causing any degradation of performance, even when the network expands, and it can minimize information exchange between nodes because only the location information of neighbor nodes is used for routing. However, since they deliver the message using the planar graph connected with short edges, a problem with increasing hop count occurs when the message is delivered sequentially along the face boundary. In particular, in a high density WSN, the number of nodes to be passed through increases, resulting in sharp performance degradation. ProgressFace [25] and Concurrent Face Routing (CFR) [26] have improved the performance and efficiency of early face routing by modifying how to forward the message instead of adjusting how to change the face. ProgressFace alleviates the problem of too many hops being taken if messages are forwarded in the wrong direction due to the unbalanced deployment of the nodes. It finds the direction with the smallest number of hops through an additional traversal step and improves routing efficiency by setting the forwarding direction to the way it finds, after which it sends the message. CFR focuses on the speed of message delivery and accelerates message propagation by sending messages concurrently in both directions of faces intersecting with line \(\overline{st}\). It can send messages to the destination via the shortest possible route because it disseminates them through all available routes via the faces adjacent to line \(\overline{st}\). Although it sends many duplicate messages to the network, it improves routing performance by sending messages at speeds similar to those sent by the shortest path. They have improved the performance, efficiency, and speed of routing by adjusting the search direction, using an additional traversal step, or forwarding duplicate messages. However, since they forward messages by sequentially exploring all the nodes constituting a face regardless of radio range, performance rapidly deteriorates due to the increased number of nodes that need to be traversed in high density WSNs. In order to improve the forwarding efficiency by considering radio range, face routing using all of the node information within two hops has been proposed [19].