Universally Hard Hamiltonian Cycle Problem Instances
Joeri Sleegers, Sarah L. Thomson, Daan van den Berg · 2022
In 2021, evolutionary algorithms found the hardest-known yes and no instances for the Hamiltonian cycle problem. These instances, which show regularity patterns, require a very high number of recursions for the best exact backtracking algorithm (Vandegriend-Culberson), but don't show up in large randomized instance ensembles. In this paper, we will demonstrate that these evolutionarily found instances of the Hamiltonian cycle problem are hard for all major backtracking algorithms, not just the Vandegriend-Culberson. We compare performance of these six algorithms on an ensemble of 91,000 randomized instances plus the evolutionar-ily found instances. These results present a first glance at universal hardness for this NP-complete problem. Algorithms, source code, and input data are all publicly supplied to the community.