A data structure is a repository of information; the goal is to organize the data so that it needs less storage (space) and so that a request for information (query) can be processed quickly. A geometric data structure handles data which have locations attached (e.g. addresses of fire stations in the state of Massachusetts). Geometric data structures have become a pervasive and integral part of life, and can be queried to produce driving directions or the name of the nearest Italian restaurant. Since the space and query time of a data structure depend upon the type of queries it needs to support, it is important to study which tools and techniques are suitable for which data structures. The ongoing quest for better data structures sometimes results in improved methods and sometimes results in entirely new techniques. The goal is to determine optimal data structures with the best possible performance. Given a set S of n points in Rd, a data structure for geometric range searching may report: whether the query range contains any point (emptiness), the number of points in the range (counting), all points in the range (reporting), or the minimum/maximum point