A 25-Year-Old Blind Spot in How Computers Measure Distance Has Finally Been Fixed, and It Matters Less Than You Think, Which Is the Point

GANDHINAGAR, INDIA — For twenty-five years, the fastest known way for a computer to estimate the distance between two points in a huge network had a blind spot, and the blind spot was, for the most part, exactly the kind of short, local trip the method was most likely to be asked about. A researcher at the Indian Institute of Technology Gandhinagar has now closed the gap, a result that is, in the words of one theorist, “the kind of thing that makes you feel, for a brief moment, that the field is actually moving forward.”

The problem is the All-Pairs Shortest Paths problem, or APSP — the task of calculating the shortest distance between every pair of points in a network. It is the problem your navigation app is already solving, except the app does it one trip at a time, while APSP does it for every trip at once. For dense networks, doing it exactly takes cubic time: double the number of points and the work goes up about eightfold. So computer scientists have spent decades building approximation algorithms — methods that trade a little precision for a lot of speed.

In 1996, Dor, Halperin, and Zwick introduced the method that became the standard, known as the DHZ algorithm. It works by picking a small handful of sample points and using them as landmarks. If two points are far apart, a landmark is likely to sit near the shortest path, and the estimate stays within a factor of two of the true distance. If two points are close, no landmark is likely to sit near the shortest path, and the estimate can blow up well past the factor of two.

The blind spot, in other words, was the neighbourhood. The algorithm could tell you, with a firm mathematical guarantee, roughly how far it was from New York to Los Angeles. It could not, with the same guarantee, tell you roughly how far it was from one suburb to the next — which is to say the algorithm was best at the trips almost no one asks about, and worst at the trips everyone asks about. The boundary between the two had resisted improvement for nearly a quarter century.

The fix, presented at the 66th Annual Symposium on Foundations of Computer Science, is a multi-scale sampling strategy. Instead of sampling the network at one scale, the new algorithm samples it at several, each layer capturing a different level of the graph’s structure. The result is that an appropriate reference point is likely to be available even when the shortest path is short — which means the algorithm can now give its factor-of-two guarantee for much closer pairs than before, while keeping the same runtime.

The result is a theoretical advance, which is to say it is not, in fact, a new feature in your navigation app. Your navigation app has not changed. But theoretical advances have a way of becoming practical ones, the way a 1996 theoretical advance became the algorithm that, for twenty-five years, was the algorithm. The improvement strengthens the foundation under internet routing, transportation planning, social platforms, and the AI systems that process relationships between connected data — the quiet engines that keep the connected systems running smoothly, which is to say it matters less than you think, which is the point.

At press time, the navigation app had not been updated, the network had not been resampled, and the blind spot had, for the first time in twenty-five years, been closed. The thing that was a thing for a quarter century is now a thing that has been fixed, which is to say the fix is now the thing.