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Finding the Maximum Independent Set: NP-Hard Problems and Performance Many programmers, upon hearing a problem is NP-Hard, assume that optimizations for exact solutions are impossible or pointless. However, it is important to keep in mind that while NP-Hard problems are non-polynomial in the worst case, the average case can be improved beyond that. Additionally, ``non-polynomial'' encompasses a wide class of running times, some of which are much more feasible than others. This article looks at a well-known NP-hard problem and iteratively optimizes a solution, presenting a final implementation that is thousands of times faster than a naive approach for some small input sets, and makes it possible to process data sets that would otherwise be intractible.