Way back when I was analysing London house price data for the Summer Data Challenge, I made a histogram of the distances from a random point in London to the nearest tube station. I noted that it peaked around half a kilometre, but ignored the shape of the distribution itself. This is an unfortunate faux pas for the accomplished procrastinator, so let’s right that wrong with the help of some stochastic geometry.
I was reading the other day about the Tube Challenge, where people attempt to visit all 270 stations on the London Underground in the quickest possible time. Apparently successful routes are a closely-guarded secret, which got me thinking about how difficult an optimisation problem it must be to find the best route.