Path planning for mobile robotics is a topic that has been studied for many decades, with many different formulations and goals. Considering obstacle avoidance with the very simple goal of minimizing the path distance from a start to end location, even this focused problem has attracted many solutions. The aspect of the problem studied in detail here is motivated by the question: what extent of the map needs to be considered by an algorithm to guarantee that the shortest path solution is within the considered extent? The algorithm presented in this paper examines this question in detail, revealing that the area of consideration can be calculated in stages of progress through a known map. Using this bound, the paper then proposes a method for guaranteeing the shortest path, while attempting to minimize the calculation time and memory requirements caused by consideration of map areas that would not admit the optimal path.