Rules of thumb
Start at 114 Delancey Street and work your way counter-clockwise around the island. Stay generally east of Broadway on the way up to Inwood. Come back down for the remaining restaurants. Finish at 160 Broadway. Plan your start time and pace to make it to McDonald’s that are not open 24 hours.
Computer simulations
The shortest route between any significant number of destinations is a surprisingly hard problem called the Traveling Salesman Problem or TSP. It’s so hard that even the world’s biggest computers can’t just try all the routes and compare them. McTrot adds another bit of complexity in that not all McDonald’s are open 24 hours. The shortest route is no use if it leads to restaurants that aren’t open. This variation of the problem has been named TSP with Time Windows, or TSP+TW.
In practice, problems of this kind are often solved with a search technique, simulated annealing, that tries making random improvements to a random route. For McTrot, you’ll also need McDonald’s location data and a geospatial dataset of walkable paths along sidewalks and trails. Fortunately, these are available on the McDonald’s website and the NYC Office of Technology and Innovation’s NYC Planimetric Database, respectively.
Software for running these simulations is available in the windmountain/mctrot GitHub repository. E-mail admin@mctrot.nyc for help using it.