Polychronous Oscillatory Cellular Neural Networks for Solving Graph Coloring Problems

This paper presents polychronous oscillatory cellular neural networks, designed for solving graph coloring problems. We propose to apply the Potts model to the four-coloring problem, using a network of locally connected oscillators under superharmonic injection locking. Based on our mapping of the Potts model to injection-locked oscillators, we utilize oscillators under divide-by-4 injection locking. Four possible states per oscillator are encoded in a polychronous fashion, where the steady state oscillator phases are analogous to the time-locked neuronal firing patterns of polychronous neurons. We apply impulse sensitivity function (ISF) theory to model and optimize the high-order injection locking of the oscillators. CMOS circuit design of a polychronous oscillatory neural network is presented, and coloring of a geographic map is demonstrated, with simulation results and design guidelines. There is good agreement between theory and Spectre simulation.