The snake-in-the-box problem: a new upper bound
Discrete Mathematics
Using the genetic algorithm to find snake-in-the-box codes
IEA/AIE '94 Proceedings of the 7th international conference on Industrial and engineering applications of artificial intelligence and expert systems
Phenotype feedback genetic algorithm operators for heuristic encoding of snakes within hypercubes
Proceedings of the 12th annual conference on Genetic and evolutionary computation
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With applications in coding theory and hypercube-based computing and networking, the "snake in the box" problem is of great practical importance. Moreover, it is both mathematically elegant and highly difficult. The problem is simply to find the longest "snake" in a hypercube. However, as the hypercube grows in dimensionality, the size of the search space increases exponentially. Moreover, as the maximum snake length is only known for the smallest dimensions (where the snakes themselves have already been identified), there is no known stopping criterion for the search in higher dimensions. In this paper we make a mathematical conjecture about the possible maximum length of a snake in a hypercube of dimension d. We use a genetic algorithm for finding snakes in a 8 hypercube to show some results.