  We present several modifications to the previously proposed MSPP algorithm
that can speed-up its execution considerably. The MSPP algorithm leverages a
multiscale representation of the environment in $n$ dimensions. The information
of the environment is stored in a tree data structure representing a recursive
dyadic partitioning of the search space. The information used by the algorithm
is the probability that a node in the tree corresponds to an obstacle in the
search space. Such trees are often created from mainstream perception
algorithms, and correspond to quadtrees and octrees in two and three
dimensions, respectively. 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 theoretical upperbound
of the probability of failure as a function of the number of samples.
