The DNA of snakes

Abstract

The Snake in the Box problem is an NP-Hard problem. The goal is to find the longest maximal snakes (a certain kind of path satisfying particular constraints described as “spread”) in an n-dimensional hypercube [8]. With increasing dimensions the search space grows exponentially and the search for snakes becomes more and more difficult. This article identifies an underlying pattern among the known longest snakes in previously searched dimensions, which resembles the DNA of living cells in many ways. Surprisingly, these generic structures are fundamentally different for the four combinations of odd and even dimension and spread. It briefly explains the reason why they have different underlying structures. In odd dimensions with odd spread, there is one symmetric point and a unique mapping of complementary transition pairs and are discussed in detail in this paper. This article focusses only on one of these - odd dimension with odd spread. Later, it also reports three new lower bounds that are established using these generic structures from previously known longest maximal snakes. Another known longest snake in another odd dimension with odd spread is also found using this approach.