Vectored Route-Length Minimization – a Heuristic and an Open Conjecture

We have posed a simple but interesting graph theoretic problem and posited a heuristic solution procedure, which we have christened as Vectored Route-length Minimization Search (VeRMinS). Basically, it constitutes of a re-casting of the classical “shortest route ” problem within a strictly Euclidean space. We have only presented a heuristic solution process with the hope that a formal proof will eventually emerge as the problem receives wider exposure within mathematical circles. Key words: graph theory, Euclidean space, network connectivity matrix A short historical background of similar class of problems The classical “shortest route ” (or shortest path) problem is properly associated with the branch of mathematics formally known as graph theory (or network theory). History has it that this theory originated in an attempt to solve a famous 18 th century routing problem concerning the Prussian city of Konigsberg (Kaliningrad in modern Russia). The city is located along the two banks and on two islands formed by the river Pregel, which effectively divides the city into four separate landmasses. Seven bridges connected the various regions of the city and the resulting “Konigsberg bridge problem ” had to do with finding an optimal route around the city that woul