Use of Cost Surface Analysis and Stream Order Analysis for Computing Shortest Paths

We find that the current state-of-the-art shortest path navigation systems have a computational bottleneck that limits their scalability. To solve this problem, our first contribution is an important result showing that two points in the environment relate to each other by more geometric criteria than just the distances between them. Our second contribution shows that the environment's geometry is such that it allows for the points in the environment to be uniquely distinguishable based on the length of the shortest paths meeting at that point. Using this result, we order the points, so their ordering uniquely distinguishes the shortest path between any source and destination pair. Through these two important results, we propose a system that solves the computational bottleneck problem using lower processing resources and has higher optimal efficiency than the state-of-the-art.