Preprocessing power weighted shortest path data using a s-Well Separated Pair Decomposition

For s > 0, we consider an algorithm that computes all s-well separated pairs in certain point sets in ℝn, n >1. For an integer K >1, we also consider an algorithm that is a permutation of Dijkstra's algorithm, that computes K-nearest neighbors using a certain power weighted shortest path metric in ℝn, n > 1. We describe each algorithm and their respective dependencies on the input data. We introduce a way to combine both algorithms into a fused algorithm. Several open problems are given for future research.