  We interleave sampling based motion planning methods with pruning ideas from
minimum spanning tree algorithms to develop a new approach for solving a
Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach
alternates between sampling points from selected regions in the search space
and de-emphasizing regions that may not lead to good solutions for MGPF. Our
approach provides an asymptotic, 2-approximation guarantee for MGPF. We also
present extensive numerical results to illustrate the advantages of our
proposed approach over uniform sampling in terms of the quality of the
solutions found and computation speed.
