The naive approach

Let us define a directed graph G=(V,E), where $V=\{\mbox{existing $k$ -mers}\}$ and an edge e=(v₁,v₂) exists iff the last k-1 characters of v₁ match the first k-1 characters of v₂. For instance, in our previous example, there will be an edge from ATG to TGC. The problem is now to find a Hamiltonian path in the directed graph G. However, as we should all be aware, this version of the traveling salesman problem is NP-hard. Therefore, this solution cannot be used for large input sets. While approximations and heuristics for the TSP exist, no true computer scientist will be satisfied with this solution.