# Xaprb

Stay curious!

## Finding things within some distance in SQL

One of the query optimization scenarios I’ve seen a lot over the years is finding something within some distance from a point. For example, finding people within some distance of yourself, apartments in a radius from a postal code, and so on.

These queries usually use the great-circle formula. That might be because Google finds lots of pages claiming that this is the right way to do a radius search. “The earth is not flat!”, they all say. That’s true, but it doesn’t mean that the great-circle formula is a good approach. It’s usually a really bad approach, in fact. It’s needlessly precise for most things, not precise enough for others, and it’s an expensive query to execute; all the trig functions tend to eat a bunch of CPU, and make it impossible to use ordinary indexes. This is true for all of the databases I’ve used — MySQL, Postgres, and SQL Server.

The great-circle formula is needlessly precise for a few reasons:

1. Within the radiuses I’ve usually seen, the earth is flat, or close enough that it doesn’t make a difference. Looking for an apartment within 25 miles of downtown? The error introduced by pretending that the earth is flat on such a small scale doesn’t matter. The Pythagorean theorem would work just as well.
2. “Downtown” is not a point, it’s an area. Nobody is going to argue if you return search results that vary by a few miles, or even more.
3. Nobody drives in a straight line from downtown to their apartment. People usually search within a physical radius as a proxy for “find me something conveniently close.” They don’t really expect the miles as-the-crow-flies to be a good proxy — it’s just one they’re used to. In reality, that apartment just across the river might be too far away from work, because you’d have to drive a long way to get to a bridge. (Unless you want to swim to the office every day, that is.)

In cases where you really do need precision, there’s a reasonable chance that the great-circle formula still isn’t right for you, because not only is the earth not flat, the earth isn’t a sphere either.

What’s the optimization I usually suggest? It’s usually perfectly acceptable to just return results within a square centered on the point of interest. In most cases, the results will be just as satisfactory to the users. The remainder are usually very special cases.

Written by Baron Schwartz

January 2nd, 2011 at 4:59 pm