MBTA speedrun

for the massachusetts bay transit authority green line, an exhaustive computer search was used to determine the fastest route which passes through every station.

routing

the green line in isolation is ammenable to interesting yet exhaustive search: it is mostly linear with obvious endpoints, but with enough branching in the middle to make the exact optimal path non-obvious, and so its verification meaningful.

the route contains 64 unique stations. the vast majority of stations are only connected to their immediate neighbors: a significant pruning of the search space is possible by breaking the route into a much smaller number legs. this is complicated by a question of taste: should on-foot transfers be allowed, or should routes stay fully on-track? compare the system's official schematic rendering (below) with the spatial map (above): it seems equitable

the timetable was encoded, and an off-the-shelf traveling saleseman (wikipedia.org) software package was used to complete an exhaustive search. the computed optimal route is given below along with intermediate timings. the ideal completion time was 2 hours and 20 minutes; in practice 2 hours 37 minutes was achieved.

further

the entirety of the MBTA system has been similarly traveled both prior and since. interest first seemed primarily in the required endurance, more recently a number of increasingly competitive attempts have been made.

the number of stations has since increased, meaning this record is now obsolete (and non-contestable.)

thanks to my good friend Eddie Z: for your enthusiasm and company during this pointless early-morning exercise; and congratulations for the first such completion of the san francisco MUNI system (transitruns.org).