All Near Neighbor GraphWithout Searching

Abstract

Given a collection of n objects equipped with a distance function d(·, ·), the Nearest Neighbor Graph (NNG) consists in finding the nearest neighbor of each object in the collection. Without an index the total cost of NNG is quadratic. Using an index the cost would be sub-quadratic if the search for individual items is sublinear. Unfortunately, due to the so called curse of dimensionality the indexed and the brute force methods are almost equally inefficient. In this paper we present an efficient algorithm to build the Near Neighbor Graph (nNG), that is an approximation of NNG, using only the index construction, without actually searching for objects.