All Near Neighbor GraphWithout Searching

Abstract

Given a collection ofnobjects equipped with a dis-tance functiond(·,·), the Nearest Neighbor Graph(NNG) consists in finding the nearest neighbor ofeach object in the collection. Without an index thetotal cost of NNG is quadratic. Using an index thecost would be sub-quadratic if the search for indi-vidual items is sublinear. Unfortunately, due to theso calledcurse of dimensionalitythe indexed and thebrute force methods are almost equally inefficient. Inthis paper we present an efficient algorithm to buildthe Near Neighbor Graph (nNG), that is an approx-imation of NNG, using only the index construction,without actually searching for objects.