Many linear search and evacuation problems have been studied on robots that move with unit speed seeking to evacuate through an unknown exit located on a line. It is interesting to study the linear search and evacuation problems on robots with variable maximum speed in order to compare the results based on that speed. What makes the problem more interesting is to include a passive entity, such as a bike, that can be used by any of the robots. This will make the problem more generalized and thus

more »

... it may encompass many previously done studies on linear search and evacuation, as we will demonstrate later. We will revisit the linear search and evacuation problems; however, this time we will use two robots with a bike under the condition that only one robot can use the bike at a time. The exit would be placed at an unknown position on the line. The direction that the robot should follow to reach the exit is unknown. The problem will be divided into two categories: linear search and evacuation. Evacuation in turn will be studied for two communication models: wi-fi and face-to-face. Regarding the linear search problem, we have shown two different algorithms that are optimal (relative to the upper bound) based on the maximum speed. Additionally, we provided a section related to the lower bound. Regarding the wi-fi evacuation model, we have shown three different algorithms, two of which are optimal (relative to the upper bound) based on the maximum speed. Furthermore, we have also provided the lower bound for the wi-fi model. Regarding the face-toface model, we have shown three different algorithms (relative to the upper bound), one of which is optimal regardless of the value of the maximum speed. Many graphs have been provided to illustrate how each model performs.