I did somewhat of a deep dive on this topic recently and found something called Euler Path and Euler Circuits. It’s a graph theory which seemed to be the answer to this question, but I quickly discovered it is way to abstract for something specific to a standard street grid. Overlapping becomes necessary as soon as there are three 3 square blocks in sequence. A Euler path would be helpful in a scenario with wacky intersections like a round-about with 6 or 7 intersecting roads or some traditional triangular style intersections.
Also, there is yet another graph theory that can be used to determine the least amount or most efficient path when overlapping. This is where I decided it is easiest to just use judgment when mapping a route. Most streets outside of an inner-city are not perfectly square and when one side is longer than the other (like a rectangle) I just opt to overlap the short-side. The human side also comes into play when thinking of efficiency in terms of elevation too.
I found the most enjoyable and efficient way is to make a route that is also easy to follow so rather than making a snaking route that overlaps itself at several points in different directions i just do a lot of down and backs on side streets as I pass them.
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