Solving the shortest path problem using an analog network

The shortest path problem is one of the most important combinatorial optimization problems. In this paper, a network consisting of variable turn-on-voltage diodes (VTDs) is proposed for tackling the shortest path problem. The network solves the shortest path problem in a parallel and distributed manner. The network itself is isomorphic to the graph in which the shortest path solution is to be sought. The proposed VTD network settles to steady-state solutions quickly and consumes very little power. It is also shown theoretically that the VTD network solves the shortest path problem exactly. A circuit implementation of the VTD network is proposed and simulation results confirm its functionality. Finally, two physical limitations of VTD´s and their effect on the performance are discussed