Nearest Neighbor Search in Multidimensional Spaces Depth Oral Report

The Nearest Neighbor Search problem is deened as follows: given a set P of n points, preprocess the points so as to eeciently answer queries that require nding the closest point in P to a query point q. If we are willing to settle for a point that is almost as close as the nearest neighbor, then we can relax the problem to the approximate Nearest Neighbor Search. Nearest Neighbor Search (exact or approximate) is an integral component in a wide range of applications that include multimedia databases, computational biology, data mining, and information retrieval. The common thread in all these applications is similarity search: given a database of objects, we want to return the object in the database that is most similar to a query object. The objects are mapped onto points in a high dimensional metric space , and similarity search reduces to a nearest neighbor search. The dimension of the underlying space may be in the order of a few hundreds, or thousands; therefore, we require algorithms that perform eeciently even for spaces of high dimension. Due to its importance, the Nearest Neighbor Search problem has been a subject of research for many decades, and in many diierent elds. In this work we survey some of the past and recent results that marked the evolution of the problem. The report starts with the optimal solutions for low-dimensional spaces, then it goes through the solutions for the exact and approximate problem for spaces of arbitrary dimension, and then it nishes oo with the recent attempts to prove lower bounds in order to specify the hardness of the problem. We also investigate the problem from the practitioner's point of view, and we provide an overview of the indexing problem for Nearest Neighbor Queries. Finally, we identify some open questions, and interesting problems.