Week 3: Approximate Near Neighbor Search

Last week we discussed the randomized O(n) expected time algorithm to compute the closest pair of points in the plane. This week we continue with a related data structure problem: (approximate) near neighbor search. Suppose you have a database D of n entries: images, text documents, census data, etc. Using a Dictionary data structure, for example a B-tree or a hash table, you can check if an entry x is in D. But sometimes you actually want to find an entry y in the database which is as “close” as possible to x, and not necessarily exactly the same. This is one of the most basic ways to do classification, for example: you keep a database of labeled images, and given a new image you want to see if it is close to any image in the database; if your new image is close to an image of a dog, then maybe it is also an image of a dog. Or, more simply, databases can contain errors, and looking for an approximate match is a way to make our database search more robust.