  The equivalence between the natural minimization of energy in a dynamical
system and the minimization of an objective function characterizing a
combinatorial optimization problem offers a promising approach to designing
dynamical system-inspired computational models and solvers for such problems.
For instance, the ground state energy of coupled electronic oscillators, under
second harmonic injection, can be directly mapped to the optimal solution of
the Maximum Cut problem. However, prior work has focused on a limited set of
such problems. Therefore, in this work, we formulate computing models based on
synchronized oscillator dynamics for a broad spectrum of combinatorial
optimization problems ranging from the Max-K-Cut (the general version of the
Maximum Cut problem) to the Traveling Salesman Problem. We show that
synchronized oscillator dynamics can be engineered to solve these different
combinatorial optimization problems by appropriately designing the coupling
function and the external injection to the oscillators. Our work marks a step
forward towards expanding the functionalities of oscillator-based analog
accelerators and furthers the scope of dynamical system solvers for
combinatorial optimization problems.
