This work studies the problem of 2-dimensional searching for the 3-sided range query of the form @math in both main and external memory, by considering a variety of input distributions. We present three sets of solutions each of which examines the 3-sided problem in both RAM and I O model respectively. The presented data structures are deterministic and the expectation is with respect to the input distribution.
Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More than ten years of spatial database research have resulted in a great variety of multidimensional access methods to support such operations. We give an overview of that work. After a brief survey of spatial data management in general, we first present the class of point access methods , which are used to search sets of points in two or more dimensions. The second part of the paper is devoted to spatial access methods to handle extended objects, such as rectangles or polyhedra. We conclude with a discussion of theoretical and experimental results concerning the relative performance of various approaches.