A Note on Mapping a Matching Problem to a Majority Network as a Lyapunov Function: Problem Solving by Synchronization

This note proposes a symmetric majority network as an energy function in discrete problem solving. As in the Lyapunov function in non-linear dynamical systems, the energy function can show convergence on stable fixed points. Similarly, the symmetric majority network, when mapped properly, can show convergence on the solution. The state transition process to the solution can also indicate a problem-solving process. As an example of discrete problem solving, a matching problem is adopted and the problem-solving process will be visualized by a simulation of a mapped majority network. The stable marriage problem, size 3 and size 4 in part, is considered and the majority network is extended to solve it