Solving hard combinatorial optimization problems such as graph coloring efficiently continues to be an outstanding challenge for computing. Traditional digital computers typically entail an exponential increase in computing resources as the problem sizes increase. This makes larger problems of practical relevance intractable to compute, with subsequently adverse implications for a broad spectrum of ever-more relevant practical applications ranging from machine learning to electronic device automation (EDA). Here, we examine how analog coupled oscillators can enable area and energy-efficient methods to accelerate such problems. Further, we discuss how the implementation of such non-Boolean platforms can take advantage of emerging technologies such as scalable ferroelectrics.