Quantifying Instance Hardness of Protein Folding within the HP-model

NP-hard problems are infamous for having highly varying and extreme runtimes for different problem instances. This study quantifies the instance hardness of NP-hard protein folding problem instances within the HP-model. A custom dataset is generated, consisting of 1000 problem instances of lengths 10, 15, 20, and 25, totalling to 4000 instances. The computational costs for solving a problem instance using a depth-first branch and bound algorithm are measured. The resulting hardness distributions can all be characterized by a probit function regardless of the corresponding protein length. Knowing the instance hardness distribution makes it possible to extrapolate the range of expected runtimes for larger problem instances. As a result, it allows for a prediction before folding a protein.