# Urban Free-Space Optical Network Optimization
## 1 Introduction
### Related Works  
In recent years, the demand for fast and available communication in urban and rural regions has increased with the rise in the use of social networks and Internet of Things devices. Therefore, a growing research has focused on optimizing communication networks. However, this paper addresses a set of network optimization problems that are relatively new. [PERSON] et al. [9] suggested a dynamic selection of communication facilities for creating connected and full-coverage networks. In their study, they used the bounded-degree nodes, instability link, and labile topology of the FSO model to build an optimization algorithm using a Voronoi diagram. [PERSON] et al. [10] suggested a proactive network reconfiguration algorithm for FSO-based fronthaul and backhaul networks. Their algorithm used mixed-integer nonlinear programming to optimize network power consumption. Those works discussed optimization of data collection from multiple sensors, made possible by the use of small low-voltage transmitters with long-term communications and precise targeting capabilities. In this paper's research, however, only two conditions are required for FSO network modeling: (1) LOS field restrictions and (2) the cost function over the nodes and FSO links. The problem of optimizing graphs presented in this work is commonly addressed as a facility location problem (see [11] for a comprehensive research regarding facility location and [12] for a recent survey on multi-criteria location problems). The classic form of this problem is defined on a graph with fixed-weight edges. The goal is to find the optimal solution (a set of vertices) for a set of facilities. A different approach to this classic model addresses the allocation of facilities on a graph with dynamic weights on the edges [13]. In other words, the alternate approach searches for an optimal registration to the graph's edges, considering all its vertices rather than searching for subsets of optimal vertices. Another related model considers finding a set of minimal vertices in a graph representing antennas on the terrain. That model defines two types of vertices in the graph, representing two types of facilities: base stations (BS) and relay stations (RS). The goal is to find a minimum set of RS that connects all the BS. The motivation for this problem is to minimize the number of antennas that must be deployed on the terrain. This problem was proven to be MAX SNP-hard (i.e., no constant approximation factor) [14]. This paper discusses a related scenario. Instead of using BS and RS, it considers a visibility graph (representing a city map) with potential and demand vertices and weights on the edges and on the vertices. Another set of problems addressed is the protocol of communication flow from the sink nodes to the leaves on an existing network while supporting longer network life. These flow problems customarily have been used in sensor-based network models where every node has limited energy. Most work on this subject dealt with the question of how to choose proper cluster head (CH) nodes in the network graph. A CH node is responsible for collecting data from the sensors and transmitting it via relay nodes. Traditionally, this problem has been solved by generating stable clusters in the mobile environment, for example, through the lower energy adaptive clustering hierarchy protocol. This grade-routing protocol uses a randomized rotation of local CHs to achieve an even distribution of energy in the network [15]. More recent research has suggested that, in many real-life cases, genetic algorithms (GAs) might lead to improved network performance [16]. In this work, the main purpose is to construct an efficient network in which the data can flow using minimum cost. In other words, instead of choosing the right CH, we want to choose the nodes that best centralize the data transmission in their area. In the network graph, that means finding the right nodes to not only cover an equal area (nodes), but also minimize the cost of this group of nodes.