Randomized trial demonstrates new record lengths for snakes in hypercubes, suggesting efficient search methods.
The Snake-in-the-Box problem seeks the longest possible induced path ("snake") in the edge graph of an n-dimensional hypercube. The best results known in hypercubes of dimension 10 or higher come from extending lower-dimensional seed snakes. This paper describes multiple methods for primed (seeded) search and presents potentially new record lengths of 1461 and 2892 for snakes in 12 and 13 dimensions, respectively.
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Thomas Ace (2026) studied this question.
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