## 1 Introduction  
The geographic routing protocol requires nodes to know the position of their neighbors for forwarding data, so each node periodically exchanges HELLO messages, including its position with its neighbors. However, periodical message exchange can be another overhead when considering the node's constraints in wireless sensor networks. Thus, in order to reduce such control overhead caused by these messages, called beacons, the beaconless geographic routing strategy has been recently studied in the literature. Different from beacon-based geographic routing protocols, typical beaconless routing [1,2] has the following process: a sender broadcasts data to its neighbors, and only neighbors in the greedy forwarding area, closer neighbors to a destination, are eligible to become next-hop forwarding candidates. Then, only one neighbor is selected as a next-hop forwarder by a completely reactive method. To avoid collision among these neighbors, the sender includes a waiting function in the data packet, which is related to the distance between each receiving neighbor and the destination. Therefore, a node having the fastest expired timer, that is the closest node from the destination among the neighbors, will become a next-hop forwarder by itself and begin to send the received data by broadcasting, as the previous sender did. The rest of the neighbors overhear this message, so they could cancel their own timer and release the received data. Besides the mentioned basic operation, we should consider abnormal situations. For example, if some of the neighbors in the greedy area cannot hear the message of other neighbors, because any two nodes may be possibly out of the radio range, it is hard to guarantee that every forwarding candidate overhears each other. This circumstance is very similar to the hidden terminal problem in the 802.11 wireless networks, and it might lead to a large number of packet duplications in such overhearing-based beaconless routing protocols, due to multiple winners among these neighbors. Therefore, in order to solve the packet duplication problem, previous studies [1,2] have tried to adopt a completely conservative approach, which reduces a forwarding candidate area to a restricted region. This approach limits the greedy forwarding area to only mutually-communicable nodes. It allows that only the nodes in the restricted forwarding area, which is nested in the greedy area, can participate in the timer-based forwarding contention. This strategy is very simple and may be effective in uniformly- and densely-deployed WSNs, but forwarding opportunities can be lost in practical WSNs. In most of the applications of WSNs, very small and inexpensive sensor nodes are deployed to an field of interest by a plane in the air. Therefore, the network commonly becomes an irregular shape that has many partial network holes due to obstacles, such as buildings, lakes, _etc_. If such holes are in the restricted small forwarding area, finding a forwarding node would fail, even if there are appropriate candidates in the rest of the area. For example, as shown in Figure 1, the sender \(S\) broadcasts its data packet to its neighbors, including both the location information of the forwarding candidate area (dashed small circle area) from the sender and position of the destination \(D\). Note that node in the forwarding candidate area tries to wait differently according to its own timer, related to the distance between the destination and itself, while nodes in the rest of the area drop the received packet from \(S\). However, in this case, there are no nodes that successfully receive the sender's broadcast data in the restricted forwarding candidate area due to both the network holes and transmission failure. Although there exist appropriate candidates in the rest of the area (Nodes\(B\) and \(C\)), the sender \(S\) has to send the data packet again or change its routing mode from the greedy mode to the recovery mode.