## 1 Introduction
The network thus has been modeled as a random-scaled sector graph (RSSG) composed of a set \(S_{n}=\{S_{i}|i=1,\,2,\,\ldots,\,n_{i}\}\) of \(n\) sensor nodes that are randomly distributed in a given area [8]. Each node with random position (\(x_{i}\), \(y_{i}\)) has a given communication radius \(r\) and a random direction \(\theta_{i}\). It can orient the active transmitting beam within a scanning area that covers a contiguous sector of \(a\) rad. This angle of the scanning area is called the scanning angle  
Figure 3: **(a)** Network parameter; **(b)**\(S_{j}\) can talk to \(S_{i}\) through multiple hops \(S_{j}\)\(S_{a}\)\(S_{b}\)\(S_{j}\). Figure 2: **(a)** An example of FSOSN; **(b)** Hierarchical network structure. and its range is \([-\frac{\pi}{2}+\theta_{i},\frac{\pi}{2}+\theta_{i}]\). Figure 3(a) shows the network parameters. Note that \(S_{i}\) and \(S_{j}\) are extracted from the network example given by Figure 3(b). For node \(S_{i}\) to hear \(S_{i}\), we must have that: \(d\left(S_{i},\,S_{j}\right)\leq r\), and \(\left(x_{j},\,y_{j}\right)\in\,\Phi_{i_{s}}\) where \(d\left(S_{i},\,S_{j}\right)\) is the Euclidean distance between nodes \(S_{i}\) and \(S_{j}\), and \(\Phi_{i}\) is the scanning area of node \(S_{i}\). Two distinct sets of neighbors are defined for each node \(S_{i}\): the set \(FNeb(S_{i})\), known as \(S_{i}\)'s forward neighborhood, contains all nodes that \(S_{i}\) can talk to directly; and the set \(BWeb(S_{i})\), known as \(S_{i}\)'s backward neighborhood, includes all nodes that can directly talk to \(S_{i}\). In Figure 3(b), \(S_{j}\) is a successor of \(S_{i}\) and \(S_{i}\) is a predecessor of \(S_{j}\)[9]. \(S_{i}\) can get to \(S_{j}\) by one hop transmission, but \(S_{j}\) has to visit \(S_{a}\) and \(S_{b}\) before reaching to \(S_{i}\). The design of algorithms and protocols for FSOSNs is very challenging. First, though current technology continues to drive the advances in sensor fabrication, including processing design and computing, advances of battery technology still lag behind, making energy resources the fundamental constraint in sensor networks, whether in RFSNs or FSOSNs. Besides, because of the large amount of nodes, recharging the battery when exhausted is unpractical for sensor network applications, particularly for those operating in hostile environments like volcanoes and swarms. Moreover, especially for FSOSNs, the property of directionality demands high network connectivity for data communication. For example, as the time goes by during data transmission, when a certain sensor node died of the depletion of energy, the network connectivity would probably drop dramatically, because the BS would lose contact with those nodes that had to go through the dead one for up-link communication. Any data originated from these nodes was meaningless and wasting energy. As a consequence, power and connectivity management becomes a main ingredient in the design of algorithms and protocols. A recent trend in wireless directional communication aims at leveraging the smart antenna, which either consists of \(N\) beam patterns or can dynamically change the direction of the beam [10,11]. Inspired by this technology, we assume that the sensor nodes in our work are able to reconfigure their direction of the active transmitter during data transmission. Accompanied with the leverage of localization techniques such as global positioning system (GPS) [12], in this paper, we propose a reconfigurable routing protocol (RRP) for FSOSNs to achieve efficient data delivery and extended lifetime by network reconfiguration. Specifically, RRP focuses on dynamically adjusting the orientation and communication radius of nodes during data transmission so as to maintain the network connectivity, guarantee packet delivery, and prolong lifetime. It works in three phases: (1) virtual topology construction, (2) routing establishment, and (3) reconfigurable routing.