Building Snakes from Dna – a Step towards Generalizing the Snake in the Box Problem

The snake in the box problem is an NP-hard problem which has been a challenging problem for both computer scientists and mathematicians. It aims to maximize certain types of paths (snakes) in a graph, an n-dimensional hypercube while satisfying certain constraints described using the concept of spread. This thesis identifies a common pattern among the longest snakes which is very similar to the DNA in living cells both structurally and functionally. It introduces a radically new approach to use this underlying pattern (the DNA) for building the longest snakes in a generalized way. By using these structures in three different dimensions three new lower bounds are established beating the previously held records. This thesis also attempts to explain why such underlying structures contribute to the longest snakes and in general how the longest snakes arrange themselves in a hypercube. INDEX WORDS: Snake-in-the-box, generalization, DNA, DNA of snake, new lower bound, higher spread, longest maximal snake BUILDING SNAKES FROM DNA – A STEP TOWARDS GENERALIZING THE SNAKE IN THE BOX PROBLEM