A discrete harmonic potential approach to motion planning on a weighted graph

A provably-correct discrete version of the harmonic potential field (HPF) approach to motion planning was suggested by Masoud, A [2006]. The approach utilizes the strong relation between graph theory and electrical network theory for developing a framework of theories and definitions that, among other things, can strongly aid in developing a discrete HPF planning approach. This framework was used to suggest an efficient, optimal, novel, discrete planning method called the M* algorithm. In this paper an in-place, successive relaxation procedure is suggested for implementing the M* algorithm. Also, the utility of the discrete HPF approach is demonstrated in robust, data network routing.