  We show that memristive networks-namely networks of resistors with memory-can
efficiently solve shortest-path optimization problems. Indeed, the presence of
memory (time non-locality) promotes self organization of the network into the
shortest possible path(s). We introduce a network entropy function to
characterize the self-organized evolution, show the solution of the
shortest-path problem and demonstrate the healing property of the solution
path. Finally, we provide an algorithm to solve the traveling salesman problem.
Similar considerations apply to networks of memcapacitors and meminductors, and
networks with memory in various dimensions.
