Priming Snake-in-the-Box Search with Seed Snakes in n-1 and n-2 Dimensions

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.