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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.

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Proximity searching is an algorithmic abstraction covering a large number of applications in areas such as machine learning, statistics, multimedia information retrieval, computer vision and pattern recognition, to name a few. The algorithmic problem consist in preprocessing a set of objects to quickly find the objects near a given query.One of the nicest algorithmic constructions in the proximity searching literature is the Spatial Approximation Tree (SAT), built with the primary design goal of approximating to the query spatially instead of using a divide and conquer approach.A key aspect in building the SAT is the order of insertion of nodes in the tree. In the plain version the nodes are inserted in increasing order of distance to the root, and this order is recursively used in the construction.In this paper we introduce the SAT + which generalizes the SAT by using an arbitrary insertion order. We tested two alternative insertion strategies improving the efficiency of the SAT at searching time.