## 1 Introduction and Literature Review
Specifically, there is a discussion of the location of United States Coast Guard helicopters that conduct SAR operations in the Atlantic Ocean [18]. In other literature, the search area is further identified by the named road network under the assumption that anyone in need of rescue would be close to the road network of a state. That is, in areas where there are large open fields, the UAV would not search throughout a-for example-cornfield. They used the road network to create a series of waypoints that can be used to route one or several UAVs through a disaster area [12]. Where tornado response begins to differentiate from other SAR response operations is that the area impacted by a tornado (that is, where people may be need of aid) is significantly smaller than the search area in an earthquake, hurricane, or even the area defined in previous work. Only about 1-5% of the area defined by a SBW is damaged. This aligns more with the wilderness and maritime SAR operations as rescuers are trying to identify a missing person or vessel in distress and identifying this is disproportionally smaller than the area needed to be searched, that is, like a \"needle-in-a-haystack\". However, wilderness and maritime SAR operations fall short because once a portion of the damaged area has been identified, the extent of the damage must also be identified. When formulating the problem as a mathematical optimization problem, the most common formulations appear to be in the form of a traveling salesperson problem [19; 20], a vehicle routing problem [21], or as a simpler shortest path problem or pathfinding problem--where returning to the start is unnecessary [22; 23; 24; 25]. While the latter papers in the literature may on the surface appear simple, the goals put forth in the papers are often to create a coverage network in an attempt to identify victims and find paths to them [25; 26], or to set up a connectivity network to a victim [24; 27]. After graph-based formulations, another common model formulation is a set covering method [28; 29]. It is a formulation well-suited to monitoring procedures as set covering formulations attempt to allocate the robots over a disaster scene to ensure connectivity [28] or to ensure an area is adequately searched [29]. Swarm-based methods (such as ant colony optimization or particle swarm optimization) are frequently used when multiple UAVs are used in completing their mission [28; 29; 30; 31; 32]. In addition to the mathematical optimization models proposed, several robot task allocation models and methods were used in the literature [1; 33; 34; 35]. Robot task allocation can be implemented in a decentralized way and enable real-time reactions to new information present in the environment. The advantage of most robot task allocations (such as in [1; 34; 35]) is that they allow for the decentralized operation of many robots. Conversely, ref. [33] allow for robots to compete for performing the next task. In addition to the well-established procedures outlined previously, some authors attempt simulation techniques such as Markov Decision Process [17; 25; 36; 37]. One method of Markov Decision Processes is conducting a random forest to determine the next area for the UAV to explore to find a lost hiker [17]. However, the method they propose works well in spatially small search areas and the attraction of the WiFi sensor helps triangulate the missing person(s). There is also use a Markov Decision Process using land-based robots are navigating an interior environment (i.e., office space, school) [36]. There is also a a Markov model attempting to predict the rescuer's needs and to deploy a UAV with wireless sensor networks and cellular networks to focus on maintaining connectivity for rescuers in a search area [37]. Markov Decision Processes can also be used to consider and map an unknown interior environment [25].