  In this work a discrete counterpart to the continuous harmonic potential
field approach is suggested. The extension to the discrete case makes use of
the strong relation HPF-based planning has to connectionist artificial
intelligence (AI). Connectionist AI systems are networks of simple,
interconnected processors running in parallel within the confines of the
environment in which the planning action is to be synthesized. It is not hard
to see that such a paradigm naturally lends itself to planning on weighted
graphs where the processors may be seen as the vertices of the graph and the
relations among them as its edges. Electrical networks are an effective
realization of connectionist AI. The utility of the discrete HPF (DHPF)
approach is demonstrated in three ways. First, the capability of the DHPF
approach to generate new, abstract, planning techniques is demonstrated by
constructing a novel, efficient, optimal, discrete planning method called the
M* algorithm. Also, its ability to augment the capabilities of existing
planners is demonstrated by suggesting a generic solution to the lower bound
problem faced by the A* algorithm. The DHPF approach is shown to be useful in
solving specific planning problems in communication. It is demonstrated that
the discrete HPF paradigm can support routing on-the-fly while the network is
still in a transient state. It is shown by simulation that if a path to the
target always exist and the switching delays in the routers are negligible, a
packet will reach its destination despite the changes in the network which may
simultaneously take place while the packet is being routed.
