Graph Coloring Using Coupled Oscillator-Based Dynamical Systems

Antik Mallick, Mohammad Khairul Bashar, Daniel S. Truesdell, Benton H. Calhoun, Siddharth Joshi, Nikhil Shukla

Abstract: Graph coloring is a NP-hard problem, and computing the solution on a digital computer entails an exponential increase in the computing resources (time, memory) with increasing problem size. This has motivated the search for alternate and more efficient non-Boolean approaches. Here, we experimentally demonstrate the solution to this problem using the phase dynamics of coupled oscillators. Using a 30-oscillator IC platform with reconfigurable all-to-all coupling and minimal post-processing, our approach achieves 98% accuracy in detecting (near-) optimal solutions within 1 color of the optimal solution in comparison to the 77% accuracy achieved with the heuristic Johnson algorithm. Additionally, we propose a new local search-based post-processing scheme to improve the quality of the coloring solution. Finally, using circuit simulations, we demonstrate the scalability and speed up (~ 100×) achievable with the above approach in larger graphs.