Unleashing the vermin (Vectored route-length minimization)

We have posed a simple but interesting graph theoretic problem and posited a heuristic solution procedure, which we have christened as Vectored Route-lenght Minimization (VeRMin). Basically, it constitutes a re-casting of the classical "shortest route" problem in a strictly Euclidean space. We have presented only a heuristic solution process hoping that a formal proof will eventually emerge as the problem receives wider exposure within mathematical circles