The naive approach

Let us define a directed graph G`=(V`,E`), where $V\lq =\{\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 (i.e., it is possible that v₂'s index in T, is the successor of v₁'s index.

The problem is now to find a Hamiltonian path in the directed graph G. However, it is a common knowledge that the Hamilonian path problem is NP-Complete. Therefore, this solution cannot be used for large input sets.