A common type of database query consists of searching according to a range of key values. Such queries are termed range queries, and the problem associated with this type of queries is known as range searching. Ranges are often defined in multiple dimensions; for example, a range query could be phrased: “Report all the people in the database who live no more than 1 km away from the market place, are between 40 and 60 years old, and whose names fall between John and Joseph in alphabetical order. This problem has a long history, and has been widely studied by the Computational Geometry community. Range searching has multiple applications on relational databases, Geographic Information Systems (GIS), Computer Graphics, networks and communication, and other areas, including other problems in Computational Geometry itself.