We present several modifications to the previously proposed MSPP algorithm that can speed-up its execution considerably. The MSPP algorithm leverages a multi-scale representation of the environment in n dimensions encoded in tree structure constructed by recursive dyadic partitioning of the search space. We first present a new method to compute the graph neighbors in order to reduce the complexity of each iteration, from O(|V|2) to O(|V| log |V|). We then show how to delay expensive intermediate computations until we know that new information will be required, hence saving time by not operating on information that is never used during the search. Finally, we present a way to remove the very expensive need to calculate a full multi-scale map with the use of sampling and derive an upper bound on the probability of failure as a function of the number of samples.

We present a path-planning algorithm that leverages a multi-scale representation of the environment. The algorithm works in n dimensions. The information of the environment is stored in a tree representing a recursive dyadic partitioning of the search space. The information used by the algorithm is the probability that a node of the tree corresponds to an obstacle in the search space. The complexity of the proposed algorithm is analyzed and its completeness is shown.